Journal articles: 'Root of unity'

1

Lötter, M. P. "Root-of-unity based signals." Electronics Letters 31, no. 24 (November 23, 1995): 2080–81. http://dx.doi.org/10.1049/el:19951423.

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2

Ip, Ivan Chi-Ho, and Masahito Yamazaki. "Quantum Dilogarithm Identities at Root of Unity." International Mathematics Research Notices 2016, no. 3 (May 20, 2015): 669–95. http://dx.doi.org/10.1093/imrn/rnv141.

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3

Han, Chirok, Peter C. B. Phillips, and Donggyu Sul. "UNIFORM ASYMPTOTIC NORMALITY IN STATIONARY AND UNIT ROOT AUTOREGRESSION." Econometric Theory 27, no. 6 (April 14, 2011): 1117–51. http://dx.doi.org/10.1017/s0266466611000016.

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While differencing transformations can eliminate nonstationarity, they typically reduce signal strength and correspondingly reduce rates of convergence in unit root autoregressions. The present paper shows that aggregating moment conditions that are formulated in differences provides an orderly mechanism for preserving information and signal strength in autoregressions with some very desirable properties. In first order autoregression, a partially aggregated estimator based on moment conditions in differences is shown to have a limiting normal distribution that holds uniformly in the autoregressive coefficient ρ, including stationary and unit root cases. The rate of convergence is $\root \of n $ when $\left| \rho \right| < 1$ and the limit distribution is the same as the Gaussian maximum likelihood estimator (MLE), but when ρ = 1 the rate of convergence to the normal distribution is within a slowly varying factor of n. A fully aggregated estimator (FAE) is shown to have the same limit behavior in the stationary case and to have nonstandard limit distributions in unit root and near integrated cases, which reduce both the bias and the variance of the MLE. This result shows that it is possible to improve on the asymptotic behavior of the MLE without using an artificial shrinkage technique or otherwise accelerating convergence at unity at the cost of performance in the neighborhood of unity. Confidence intervals constructed from the FAE using local asymptotic theory around unity also lead to improvements over the MLE.

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4

Suzuki, Takashi. "More onUq(su(1,1)) withqa root of unity." Journal of Mathematical Physics 35, no. 12 (December 1994): 6857–74. http://dx.doi.org/10.1063/1.530646.

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5

Kirby, Robion, Paul Melvin, and Xingru Zhang. "Quantum invariants at the sixth root of unity." Communications in Mathematical Physics 151, no. 3 (February 1993): 607–17. http://dx.doi.org/10.1007/bf02097030.

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6

Shi, Zhiyong. "Existence and dimensionality of simple weight modules for quantum enveloping algebras." Bulletin of the Australian Mathematical Society 48, no. 1 (August 1993): 35–40. http://dx.doi.org/10.1017/s0004972700015434.

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We give sufficient and necessary conditions for simple modules of the quantum group or the quantum enveloping algebra Uq(g) to have weight space decompositions, where g is a semisimple Lie algebra and q is a nonzero complex number. We show that(i) if q is a root of unity, any simple module of Uq(g) is finite dimensional, and hence is a weight module;(ii) if q is generic, that is, not a root of unity, then there are simple modules of Uq(g) which do not have weight space decompositions.Also the group of units of Uq(g) is found.

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7

Phillips, Peter C. B., Hyungsik Roger Moon, and Zhijie Xiao. "HOW TO ESTIMATE AUTOREGRESSIVE ROOTS NEAR UNITY." Econometric Theory 17, no. 1 (February 2001): 29–69. http://dx.doi.org/10.1017/s0266466601171021.

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A new model of near integration is formulated in which the local to unity parameter is identifiable and consistently estimable with time series data. The properties of the model are investigated, new functional laws for near integrated time series are obtained that lead to mixed diffusion processes, and consistent estimators of the localizing parameter are constructed. The model provides a more complete interface between I(0) and I(1) models than the traditional local to unity model and leads to autoregressive coefficient estimates with rates of convergence that vary continuously between the O(√n) rate of stationary autoregression, the O(n) rate of unit root regression, and the power rate of explosive autoregression. Models with deterministic trends are also considered, least squares trend regression is shown to be efficient, and consistent estimates of the localizing parameter are obtained for this case also. Conventional unit root tests are shown to be consistent against local alternatives in the new class.

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8

Dunne, R. S., A. J. Macfarlane, J. A. de Azcárraga, and J. C. Pérez Bueno. "Theq-calculus for genericq andq a root of unity." Czechoslovak Journal of Physics 46, no. 12 (December 1996): 1235–42. http://dx.doi.org/10.1007/bf01690338.

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9

Backelin, Erik, and Kobi Kremnizer. "Localization for quantum groups at a root of unity." Journal of the American Mathematical Society 21, no. 4 (June 19, 2008): 1001–18. http://dx.doi.org/10.1090/s0894-0347-08-00608-5.

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10

Spiridonov, Vyacheslav, and Alexei Zhedanov. "q-Ultraspherical polynomials for q a root of unity." Letters in Mathematical Physics 37, no. 2 (June 1996): 173–80. http://dx.doi.org/10.1007/bf00416020.

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11

Stroganov, Yu G. "Izergin-Korepin Determinant at a Third Root of Unity." Theoretical and Mathematical Physics 146, no. 1 (January 2006): 53–62. http://dx.doi.org/10.1007/s11232-006-0006-8.

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12

KAMADA, N. "QUANTUM PSU(2) INVARIANT AT A FIFTH ROOT OF UNITY." Journal of Knot Theory and Its Ramifications 05, no. 03 (June 1996): 301–10. http://dx.doi.org/10.1142/s0218216596000217.

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For Z/rZ-homology 3-spheres the Casson invariant is related to the quantum PSU (2) invariant at an rth root of unity with odd prime r. We prove a similar relationship between the Casson invariant and the quantum PSU (2) invariant at a fifth root of unity for a 3-manifold whose first Z /5 Z -Betti number is positive.

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13

Patterson, S. J. "The distribution of certain special values of the cubic Legendre symbol." Glasgow Mathematical Journal 27 (October 1985): 165–84. http://dx.doi.org/10.1017/s0017089500006169.

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Let ω be a primitive cube root of unity. We define the cubic residue symbol (Legendre symbol) on ℤ[ω] as follows. Let πεℤ[ω] be a prime, (3, π)=1. For α ε ℤ[ω] such that (α, π)=1 we let be that third root of unity so that

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14

Dou, Liyu, and Ulrich K. Müller. "Generalized Local‐to‐Unity Models." Econometrica 89, no. 4 (2021): 1825–54. http://dx.doi.org/10.3982/ecta17944.

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We introduce a generalization of the popular local‐to‐unity model of time series persistence by allowing for p autoregressive (AR) roots and p − 1 moving average (MA) roots close to unity. This generalized local‐to‐unity model, GLTU( p), induces convergence of the suitably scaled time series to a continuous time Gaussian ARMA( p, p − 1) process on the unit interval. Our main theoretical result establishes the richness of this model class, in the sense that it can well approximate a large class of processes with stationary Gaussian limits that are not entirely distinct from the unit root benchmark. We show that Campbell and Yogo's (2006) popular inference method for predictive regressions fails to control size in the GLTU(2) model with empirically plausible parameter values, and we propose a limited‐information Bayesian framework for inference in the GLTU( p) model and apply it to quantify the uncertainty about the half‐life of deviations from purchasing power parity.

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15

Itoyama, H., T. Oota, and R. Yoshioka. "q -Virasoro/W algebra at root of unity and parafermions." Nuclear Physics B 889 (December 2014): 25–35. http://dx.doi.org/10.1016/j.nuclphysb.2014.10.006.

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16

Soltanalian, Mojtaba, and Petre Stoica. "On Prime Root-of-Unity Sequences With Perfect Periodic Correlation." IEEE Transactions on Signal Processing 62, no. 20 (October 2014): 5458–70. http://dx.doi.org/10.1109/tsp.2014.2349881.

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17

Itoyama, H., T. Oota, and R. Yoshioka. "Elliptic algebra, Frenkel–Kac construction and root of unity limit." Journal of Physics A: Mathematical and Theoretical 50, no. 36 (August 11, 2017): 365401. http://dx.doi.org/10.1088/1751-8121/aa8233.

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18

Ganev, Iordan. "Quantizations of multiplicative hypertoric varieties at a root of unity." Journal of Algebra 506 (July 2018): 92–128. http://dx.doi.org/10.1016/j.jalgebra.2018.03.015.

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19

Chun, Carolyn, Dillon Mayhew, and Mike Newman. "Obstacles to Decomposition Theorems for Sixth-Root-of-Unity Matroids." Annals of Combinatorics 19, no. 1 (January 11, 2015): 79–93. http://dx.doi.org/10.1007/s00026-015-0254-0.

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20

Xia, Lingli, and Jing Yang. "Sign or root of unity ambiguities of certain Gauss sums." Frontiers of Mathematics in China 7, no. 4 (July 12, 2012): 743–64. http://dx.doi.org/10.1007/s11464-012-0217-2.

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21

Tange, Rudolf. "The centre of quantum sln at a root of unity." Journal of Algebra 301, no. 1 (July 2006): 425–45. http://dx.doi.org/10.1016/j.jalgebra.2005.11.036.

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22

Heatherly, Henry, and Altha Blanchet. "N-th root rings." Bulletin of the Australian Mathematical Society 35, no. 1 (February 1987): 111–23. http://dx.doi.org/10.1017/s0004972700013083.

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A ring for which there is a fixed integer n ≥ 2 such that every element in the ring has an n-th in the ring is called an n-th root ring. This paper gives numerous examples of diverse types of n-th root rings, some via general construction procedures. It is shown that every commutative ring can be embedded in a commutative n-th root ring with unity. The structure of n-th root rings with chain conditions is developed and finite n-th root rings are completely classified. Subdirect product representations are given for several classes of n-th root rings.

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23

Borwein, Peter, and Christopher Pinner. "Polynomials With {0, +1, -1} Coefficients and a Root Close to a Given Point." Canadian Journal of Mathematics 49, no. 5 (October 1, 1997): 887–915. http://dx.doi.org/10.4153/cjm-1997-047-3.

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AbstractFor a fixed algebraic number α we discuss how closely α can be approximated by a root of a {0, +1, -1} polynomial of given degree. We show that the worst rate of approximation tends to occur for roots of unity, particularly those of small degree. For roots of unity these bounds depend on the order of vanishing, k, of the polynomial at α.In particular we obtain the following. Let BN denote the set of roots of all {0, +1, -1} polynomials of degree at most N and BN(α k) the roots of those polynomials that have a root of order at most k at α. For a Pisot number α in (1, 2] we show thatand for a root of unity α thatWe study in detail the case of α = 1, where, by far, the best approximations are real. We give fairly precise bounds on the closest real root to 1. When k = 0 or 1 we can describe the extremal polynomials explicitly.

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24

Chao, John C., and Peter C. B. Phillips. "Uniform Inference in Panel Autoregression." Econometrics 7, no. 4 (November 26, 2019): 45. http://dx.doi.org/10.3390/econometrics7040045.

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This paper considers estimation and inference concerning the autoregressive coefficient ( ρ ) in a panel autoregression for which the degree of persistence in the time dimension is unknown. Our main objective is to construct confidence intervals for ρ that are asymptotically valid, having asymptotic coverage probability at least that of the nominal level uniformly over the parameter space. The starting point for our confidence procedure is the estimating equation of the Anderson–Hsiao (AH) IV procedure. It is well known that the AH IV estimation suffers from weak instrumentation when ρ is near unity. But it is not so well known that AH IV estimation is still consistent when ρ = 1 . In fact, the AH estimating equation is very well-centered and is an unbiased estimating equation in the sense of Durbin (1960), a feature that is especially useful in confidence interval construction. We show that a properly normalized statistic based on the AH estimating equation, which we call the M statistic, is uniformly convergent and can be inverted to obtain asymptotically valid interval estimates. To further improve the informativeness of our confidence procedure in the unit root and near unit root regions and to alleviate the problem that the AH procedure has greater variation in these regions, we use information from unit root pretesting to select among alternative confidence intervals. Two sequential tests are used to assess how close ρ is to unity, and different intervals are applied depending on whether the test results indicate ρ to be near or far away from unity. When ρ is relatively close to unity, our procedure activates intervals whose width shrinks to zero at a faster rate than that of the confidence interval based on the M statistic. Only when both of our unit root tests reject the null hypothesis does our procedure turn to the M statistic interval, whose width has the optimal N - 1 / 2 T - 1 / 2 rate of shrinkage when the underlying process is stable. Our asymptotic analysis shows this pretest-based confidence procedure to have coverage probability that is at least the nominal level in large samples uniformly over the parameter space. Simulations confirm that the proposed interval estimation methods perform well in finite samples and are easy to implement in practice. A supplement to the paper provides an extensive set of new results on the asymptotic behavior of panel IV estimators in weak instrument settings.

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25

RODRÍGUEZ-ROMO, SUEMI. "SLq(2) GLOBAL SYMMETRY FOR FOUR-STATE QUANTUM CHAINS." Modern Physics Letters A 17, no. 30 (September 28, 2002): 1999–2008. http://dx.doi.org/10.1142/s0217732302008629.

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Following the method already used to obtain quantum chains with Dipper–Donkin global symmetry,14 we obtain all possible four-state quantum chains with SL q(2,C) global symmetry when q is not a root of unity. One of these Hamiltonians is written in terms of matrix units, as an example.

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26

KUPPUM, SRIKANTH, and XINGRU ZHANG. "ROOTS OF UNITY ASSOCIATED TO STRONGLY DETECTED BOUNDARY SLOPES." Journal of Knot Theory and Its Ramifications 18, no. 12 (December 2009): 1623–36. http://dx.doi.org/10.1142/s0218216509007695.

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27

Du, Jie, Haixia Gu, and Jianpan Wang. "Irreducible representations of q-Schur superalgebras at a root of unity." Journal of Pure and Applied Algebra 218, no. 11 (November 2014): 2012–59. http://dx.doi.org/10.1016/j.jpaa.2014.03.003.

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28

Drungilas, Paulius, and Artūras Dubickas. "Multiplicative dependence of two integers shifted by a root of unity." Proceedings of the American Mathematical Society 147, no. 2 (October 31, 2018): 505–11. http://dx.doi.org/10.1090/proc/14136.

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29

Zeng, Bo, and Shaobin Tan. "Automorphism Group ofq-Quantum Torus Lie Algebra withqa Root of Unity*." Communications in Algebra 36, no. 11 (November 6, 2008): 3999–4010. http://dx.doi.org/10.1080/00927870802174264.

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30

Navarro, Gabriel, and Geoffrey R. Robinson. "Irreducible characters taking root of unity values on $p$-singular elements." Proceedings of the American Mathematical Society 140, no. 11 (November 1, 2012): 3785–92. http://dx.doi.org/10.1090/s0002-9939-2012-11242-0.

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31

Arnaudon, D., and A. Chakrabarti. "q-analogue of IU (n) for q a root of unity." Physics Letters B 255, no. 2 (February 1991): 242–48. http://dx.doi.org/10.1016/0370-2693(91)90242-i.

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32

Garoufalidis, Stavros, and Roland van der Veen. "Asymptotics of quantum spin networks at a fixed root of unity." Mathematische Annalen 352, no. 4 (April 9, 2011): 987–1012. http://dx.doi.org/10.1007/s00208-011-0662-3.

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33

Lentner, Simon. "A Frobenius homomorphism for Lusztig’s quantum groups for arbitrary roots of unity." Communications in Contemporary Mathematics 18, no. 03 (March 22, 2016): 1550040. http://dx.doi.org/10.1142/s0219199715500406.

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For a finite-dimensional semisimple Lie algebra and a root of unity, Lusztig defined an infinite-dimensional quantum group of divided powers. Under certain restrictions on the order of the root of unity, he constructed a Frobenius homomorphism with finite-dimensional Hopf kernel and with the image of the universal enveloping algebra. In this article, we define and completely describe the Frobenius homomorphism for arbitrary roots of unity by systematically using the theory of Nichols algebras. In several new exceptional cases, the Frobenius–Lusztig kernel is associated to a different Lie algebra than the initial Lie algebra. Moreover, the Frobenius homomorphism often switches short and long roots and/or maps to a braided category.

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34

Fabbri, Marc A., and Frank Okoh. "Representations of Quantum Heisenberg Algebras." Canadian Journal of Mathematics 46, no. 5 (October 1, 1994): 920–29. http://dx.doi.org/10.4153/cjm-1994-052-7.

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AbstractA Lie algebra is called a Heisenberg algebra if its centre coincides with its derived algebra and is one-dimensional. When is infinite-dimensional, Kac, Kazhdan, Lepowsky, and Wilson have proved that -modules that satisfy certain conditions are direct sums of a canonical irreducible submodule. This is an algebraic analogue of the Stone-von Neumann theorem. In this paper, we extract quantum Heisenberg algebras, q(), from the quantum affine algebras whose vertex representations were constructed by Frenkel and Jing. We introduce the canonical irreducible q()-module Mq and a class Cq of q()-modules that are shown to have the Stone-von Neumann property. The only restriction we place on the complex number q is that it is not a square root of 1. If q1 and q2 are not roots of unity, or are both primitive m-th roots of unity, we construct an explicit isomorphism between q1() and q2(). If q1 is a primitive m-th root of unity, m odd, q2 a primitive 2m-th or a primitive 4m-th root of unity, we also construct an explicit isomorphism between q1() and q2().

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35

PHILLIPS, PETER C. B. "DYNAMIC PANEL ANDERSON-HSIAO ESTIMATION WITH ROOTS NEAR UNITY." Econometric Theory 34, no. 2 (September 22, 2015): 253–76. http://dx.doi.org/10.1017/s0266466615000298.

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Limit theory is developed for the dynamic panel IV estimator in the presence of an autoregressive root near unity. In the unit root case, Anderson–Hsiao lagged variable instruments satisfy orthogonality conditions but are well known to be irrelevant. For a fixed time series sample size (T) IV is inconsistent and approaches a shifted Cauchy-distributed random variate as the cross-section sample sizen→ ∞. But whenT→ ∞, either for fixednor asn→ ∞, IV is$\sqrt T$consistent and its limit distribution is a ratio of random variables that converges to twice a standard Cauchy asn→ ∞. In this case, the usual instruments are uncorrelated with the regressor but irrelevance does not prevent consistent estimation. The same Cauchy limit theory holds sequentially and jointly as (n,T) → ∞ with no restriction on the divergence rates ofnandT.When the common autoregressive root$\rho = 1 + c/\sqrt T$the panel comprises a collection of mildly integrated time series. In this case, the IV estimator is$\sqrt n$consistent for fixedTand$\sqrt {nT}$consistent with limit distributionN(0, 4) when (n,T) → ∞ sequentially or jointly. These results are robust for common roots of the formρ= 1+c/Tγfor allγ∈ (0, 1) and joint convergence holds. Limit normality holds but the variance changes whenγ= 1. Whenγ> 1 joint convergence fails and sequential limits differ with different rates of convergence. These findings reveal the fragility of conventional Gaussian IV asymptotics to persistence in dynamic panel regressions.

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36

SIKORA, ADAM S. "SKEIN MODULES AT THE 4TH ROOTS OF UNITY." Journal of Knot Theory and Its Ramifications 13, no. 05 (August 2004): 571–85. http://dx.doi.org/10.1142/s0218216504003391.

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The Kauffman bracket skein modules, [Formula: see text], have been calculated for A=±1 for all 3-manifolds M by relating them to the [Formula: see text]-character varieties. We extend this description to the case when A is a 4th root of 1 and M is either a surface×[0,1] or a rational homology sphere (or its submanifold).

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37

ARNAUDON, DANIEL. "ON PERIODIC REPRESENTATIONS OF QUANTUM GROUPS." International Journal of Modern Physics B 06, no. 11n12 (June 1992): 1873–80. http://dx.doi.org/10.1142/s0217979292000918.

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We present some results on representations of quantum groups at the root of unity. In the case of SL(2)q, the classification of the finite dimensional irreducible representations is given. For [Formula: see text] with [Formula: see text] a semi-simple or affine Lie algebra and q an mth root of unity (m odd), we classify the representations of dimension [Formula: see text] on which the actions of the Chevalley generators are injective. Finally, we adapt the Gelfand-Zetlin basis to the case of SL(N)q and IU(N)q.

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38

Tanisaki, Toshiyuki. "Differential operators on quantized flag manifolds at roots of unity, II." Nagoya Mathematical Journal 214 (June 2014): 1–52. http://dx.doi.org/10.1017/s0027763000010837.

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AbstractWe formulate a Beilinson-Bernstein-type derived equivalence for a quantized enveloping algebra at a root of 1 as a conjecture. It says that there exists a derived equivalence between the category of modules over a quantized enveloping algebra at a root of 1 with fixed regular Harish-Chandra central character and the category of certain twistedD-modules on the corresponding quantized flag manifold. We show that the proof is reduced to a statement about the (derived) global sections of the ring of differential operators on the quantized flag manifold. We also give a reformulation of the conjecture in terms of the (derived) induction functor.

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39

Tanisaki, Toshiyuki. "Differential operators on quantized flag manifolds at roots of unity, II." Nagoya Mathematical Journal 214 (June 2014): 1–52. http://dx.doi.org/10.1215/00277630-2402198.

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AbstractWe formulate a Beilinson-Bernstein-type derived equivalence for a quantized enveloping algebra at a root of 1 as a conjecture. It says that there exists a derived equivalence between the category of modules over a quantized enveloping algebra at a root of 1 with fixed regular Harish-Chandra central character and the category of certain twisted D-modules on the corresponding quantized flag manifold. We show that the proof is reduced to a statement about the (derived) global sections of the ring of differential operators on the quantized flag manifold. We also give a reformulation of the conjecture in terms of the (derived) induction functor.

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40

Waterhouse, William C. "The Normal Closures of Certain Kummer Extensions." Canadian Mathematical Bulletin 37, no. 1 (March 1, 1994): 133–39. http://dx.doi.org/10.4153/cmb-1994-019-4.

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AbstractLet F be a field containing a primitive p-th root of unity, let K / F be a cyclic extension with group 〈σ〉 of order pn, and choose a in K. This paper shows how the Galois group of the normal closure of K(a1/p) over F can be determined by computations within K. The key is to define a sequence by applying the operation x ↦ σ(x)/x repeatedly to a. The first appearance of a p-th power determines the degree of the extension and restricts the Galois group to one or two possibilities. A certain expression involving that p-th root and the terms in the sequence up to that point is a p-th root of unity, and the group is finally determined by testing whether that root is 1. When (σ(a)/a G Kp, the results reduce to a theorem of A. A. Albert on cyclic extensions.

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41

Zacharasiewicz, Waldemar, and John Kenny Crane. "The Root of all Evil: The Thematic Unity of William Styron's Fiction." American Literature 58, no. 3 (October 1986): 459. http://dx.doi.org/10.2307/2925634.

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42

Petersen, Jens Ulrik Holger. "The centre of a quantum affine algebra at a root of unity." Czechoslovak Journal of Physics 44, no. 11-12 (November 1994): 1091–100. http://dx.doi.org/10.1007/bf01690461.

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43

Xiao, Zhijie. "LIKELIHOOD-BASED INFERENCE IN TRENDING TIME SERIES WITH A ROOT NEAR UNITY." Econometric Theory 17, no. 6 (December 2001): 1082–112. http://dx.doi.org/10.1017/s0266466601176036.

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This paper studies likelihood-based estimation and tests for autoregressive time series models with deterministic trends and general disturbance distributions. In particular, a joint estimation of the trend coefficients and the autoregressive parameter is considered. Asymptotic analysis on the M-estimators is provided. It is shown that the limiting distributions of these estimators involve nonlinear equation systems of Brownian motions even for the simple case of least squares regression. Unit root tests based on M-estimation are also considered, and extensions of the Neyman–Pearson test are studied. The finite sample performance of these estimators and testing procedures is examined by Monte Carlo experiments.

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44

Cooney, Nicholas, Iordan Ganev, and David Jordan. "Quantum Weyl algebras and reflection equation algebras at a root of unity." Journal of Pure and Applied Algebra 224, no. 12 (December 2020): 106440. http://dx.doi.org/10.1016/j.jpaa.2020.106440.

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45

Itoyama, H., T. Oota, and R. Yoshioka. "q-Virasoro algebra at root of unity limit and 2d-4d connection." Journal of Physics: Conference Series 474 (November 29, 2013): 012022. http://dx.doi.org/10.1088/1742-6596/474/1/012022.

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46

Khovanov, Mikhail. "Hopfological algebra and categorification at a root of unity: The first steps." Journal of Knot Theory and Its Ramifications 25, no. 03 (March 2016): 1640006. http://dx.doi.org/10.1142/s021821651640006x.

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Any finite-dimensional Hopf algebra [Formula: see text] is Frobenius and the stable category of [Formula: see text]-modules is triangulated monoidal. To [Formula: see text]-comodule algebras we assign triangulated module-categories over the stable category of [Formula: see text]-modules. These module-categories are generalizations of homotopy and derived categories of modules over a differential graded algebra. We expect that, for suitable [Formula: see text], our construction could be a starting point in the program of categorifying quantum invariants of 3-manifolds.

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47

Roan, Shi-shyr. "TheQ-operator for root-of-unity symmetry in the six-vertex model." Journal of Physics A: Mathematical and General 39, no. 40 (September 19, 2006): 12303–25. http://dx.doi.org/10.1088/0305-4470/39/40/002.

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48

McGerty, Kevin. "Langlands Duality for Representations and Quantum Groups at a Root of Unity." Communications in Mathematical Physics 296, no. 1 (February 4, 2010): 89–109. http://dx.doi.org/10.1007/s00220-010-0993-z.

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49

Liu, Xufeng. "A New Aspect of Representations of Uq(sl̂2)—Root of Unity Case." Journal of Algebra 243, no. 1 (September 2001): 1–15. http://dx.doi.org/10.1006/jabr.2001.8825.

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50

De Brabanter, Kris, and Farzad Sabzikar. "Asymptotic theory for regression models with fractional local to unity root errors." Metrika 84, no. 7 (March 11, 2021): 997–1024. http://dx.doi.org/10.1007/s00184-021-00812-7.

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Journal articles on the topic 'Root of unity'

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