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Journal articles on the topic 'Modules de Verma généralisés'

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Published: 4 June 2021
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1

Eastwood, Michael, and Jan Slovák. "Semiholonomic Verma Modules." Journal of Algebra 197, no. 2 (November 1997): 424–48. http://dx.doi.org/10.1006/jabr.1997.7136.

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2

Brion, Michel. "Plethysm and Verma Modules." Journal of the London Mathematical Society 52, no. 3 (December 1995): 449–66. http://dx.doi.org/10.1112/jlms/52.3.449.

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3

Carlin, Kevin J. "Extensions of Verma modules." Transactions of the American Mathematical Society 294, no. 1 (January 1, 1986): 29. http://dx.doi.org/10.1090/s0002-9947-1986-0819933-4.

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4

Billig, Y., V. Futorny, and A. Molev. "Verma Modules for Yangians." Letters in Mathematical Physics 78, no. 1 (September 1, 2006): 1–16. http://dx.doi.org/10.1007/s11005-006-0107-1.

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5

Khomenko, Oleksandr, and Volodymyr Mazorchuk. "Generalized Verma Modules Induced from sl(2,C) and Associated Verma Modules." Journal of Algebra 242, no. 2 (August 2001): 561–76. http://dx.doi.org/10.1006/jabr.2001.8815.

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6

Khomenko, Oleksandr, and Volodymyr Mazorchuk. "Rigidity of generalized Verma modules." Colloquium Mathematicum 92, no. 1 (2002): 45–57. http://dx.doi.org/10.4064/cm92-1-4.

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7

Geiss, Christof, Bernard Leclerc, and Jan Schröer. "Verma Modules and Preprojective Algebras." Nagoya Mathematical Journal 182 (June 2006): 241–58. http://dx.doi.org/10.1017/s002776300002688x.

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AbstractWe give a geometric construction of the Verma modules of a symmetric Kac-Moody Lie algebra g in terms of constructible functions on the varieties of nilpotent finite-dimensional modules of the corresponding preprojective algebra Λ.
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8

Tan, Yilan. "Verma modules for twisted Yangians." Communications in Algebra 48, no. 1 (July 14, 2019): 210–17. http://dx.doi.org/10.1080/00927872.2019.1640235.

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9

Boe, Brian D. "Homomorphisms between generalized Verma modules." Transactions of the American Mathematical Society 288, no. 2 (February 1, 1985): 791. http://dx.doi.org/10.1090/s0002-9947-1985-0776404-0.

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10

Mazorchuk, Volodymyr. "Tableaux Realization of Generalized Verma Modules." Canadian Journal of Mathematics 50, no. 4 (August 1, 1998): 816–28. http://dx.doi.org/10.4153/cjm-1998-043-x.

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AbstractWe construct the tableaux realization of generalized Verma modules over the Lie algebra sl(3, ℂ). By the same procedure we construct and investigate the structure of a new family of generalized Verma modules over sl(n, ℂ).
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11

Kable, Anthony C. "Deficient homomorphisms between generalized Verma modules." International Journal of Mathematics 30, no. 11 (October 2019): 1950056. http://dx.doi.org/10.1142/s0129167x19500563.

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A class of homomorphisms between generalized Verma modules that have an unusual degeneracy is identified. Homomorphisms in this class are called deficient homomorphisms. A family of maximally deficient homomorphisms is constructed. A necessary condition on a parabolic subalgebra is identified for the associated category of generalized Verma modules to admit deficient homomorphisms.
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12

Wang, Xian-Dong, and Kaiming Zhao. "Verma modules over Virasoro-like algebras." Journal of the Australian Mathematical Society 80, no. 2 (April 2006): 179–91. http://dx.doi.org/10.1017/s1446788700013069.

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AbstractLet K be a field of characteristic 0, G the direct sum of two copies of the additive group of integers. For a total order ≺ on G, which is compatible with the addition, and for any ċ1, ċ2 ∈ K, we define G-graded highest weight modules M(ċ1, ċ2, ≺) over the Virasoro-like algebra , indexed by G. It is natural to call them Verma modules. In the present paper, the irreducibility of M (ċ1, ċ2, ≺) is completely determined and the structure of reducible module M (ċ1, ċ2, ≺)is also described.
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13

Baston, R. J. "Verma modules and differential conformal invariants." Journal of Differential Geometry 32, no. 3 (1990): 851–98. http://dx.doi.org/10.4310/jdg/1214445537.

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14

Cox, B., V. Futorny, S.-J. Kang, and D. Melville. "Quantum Deformations of Imaginary Verma Modules." Proceedings of the London Mathematical Society 74, no. 1 (January 1997): 52–80. http://dx.doi.org/10.1112/s0024611597000038.

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15

Britten, D. J., V. M. Futorny, and F. W. Lemire. "Submodule Lattice of Generalized Verma Modules." Communications in Algebra 31, no. 12 (January 12, 2003): 6175–97. http://dx.doi.org/10.1081/agb-120024874.

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16

Musson, Ian M. "Twisting functors and generalized Verma modules." Proceedings of the American Mathematical Society 147, no. 3 (December 7, 2018): 1013–22. http://dx.doi.org/10.1090/proc/14310.

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17

Li, Yiyang, Bin Shu, and Yufeng Yao. "Support varieties of baby Verma modules." Journal of Algebra and Its Applications 17, no. 11 (November 2018): 1850211. http://dx.doi.org/10.1142/s0219498818502110.

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Let [Formula: see text] be a connected reductive algebraic group over an algebraically closed field [Formula: see text] of prime characteristic [Formula: see text] and [Formula: see text]. For a given nilpotent [Formula: see text]-character [Formula: see text], let [Formula: see text] be a baby Verma module associated with a restricted weight [Formula: see text]. A conjecture describing the support variety of [Formula: see text] via that of its restricted counterpart is given: [Formula: see text]. Under the assumption of [Formula: see text](the Coxeter number) and [Formula: see text] [Formula: see text]-regular, this conjecture is proved when [Formula: see text] falls in the regular nilpotent orbit for any [Formula: see text] and the subregular nilpotent orbit for [Formula: see text] being of type [Formula: see text]. We also verify this conjecture whenever [Formula: see text] is of type [Formula: see text] and [Formula: see text] falls in the minimal nilpotent orbit.
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18

Gyoja, Akihiko. "Further generalization of generalized Verma modules." Publications of the Research Institute for Mathematical Sciences 29, no. 3 (1993): 349–95. http://dx.doi.org/10.2977/prims/1195167048.

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19

Farnsteiner, R., and G. Röhrle. "Almost split sequences of Verma modules." Mathematische Annalen 322, no. 4 (April 1, 2002): 701–43. http://dx.doi.org/10.1007/s002080100279.

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20

Futorny, Vyacheslav M., and Duncan J. Melville. "Equivalence of certain categories of modules for quantized affine lie algebras." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 69, no. 2 (October 2000): 162–75. http://dx.doi.org/10.1017/s1446788700002159.

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AbstractWe show that a quantum Verma-type module for a quantum group associated to an affine Kac-Moody algebra is characterized by its subspace of finite-dimensional weight spaces. In order to do this we prove an explicit equivalence of categories between a certain category containing the quantum Verma modules and a category of modules for a subalgebra of the quantum group for which the finite part of the Verma module is itself a module.
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21

Khomenko, Oleksandr, and Volodymyr Mazorchuk. "Structure of Modules Induced from Simple Modules with Minimal Annihilator." Canadian Journal of Mathematics 56, no. 2 (April 1, 2004): 293–309. http://dx.doi.org/10.4153/cjm-2004-014-5.

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AbstractWe study the structure of generalized Verma modules over a semi-simple complex finite-dimensional Lie algebra, which are induced from simple modules over a parabolic subalgebra. We consider the case when the annihilator of the starting simple module is a minimal primitive ideal if we restrict this module to the Levi factor of the parabolic subalgebra. We show that these modules correspond to proper standard modules in some parabolic generalization of the Bernstein-Gelfand-Gelfand category and prove that the blocks of this parabolic category are equivalent to certain blocks of the category of Harish-Chandra bimodules. From this we derive, in particular, an irreducibility criterion for generalized Verma modules. We also compute the composition multiplicities of those simple subquotients, which correspond to the induction from simple modules whose annihilators are minimal primitive ideals.
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22

Matumoto, Hisayosi. "On the homomorphisms between scalar generalized Verma modules." Compositio Mathematica 150, no. 5 (March 26, 2014): 877–92. http://dx.doi.org/10.1112/s0010437x13007677.

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AbstractIn this article, we study the homomorphisms between scalar generalized Verma modules. We conjecture that any homomorphism between scalar generalized Verma modules is a composition of elementary homomorphisms. The purpose of this article is to confirm the conjecture for some parabolic subalgebras under the assumption that the infinitesimal characters are regular.
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23

Wen, Xin. "Representations of 𝔰𝔩3 in characteristic 3." Journal of Algebra and Its Applications 16, no. 01 (January 2017): 1750012. http://dx.doi.org/10.1142/s0219498817500128.

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Let [Formula: see text] be the special linear Lie algebra [Formula: see text] of rank 2 over an algebraically closed field [Formula: see text] of characteristic 3. In this paper, we classify all irreducible representations of [Formula: see text], which completes the classification of the irreducible representations of [Formula: see text] over an algebraically closed field of arbitrary characteristic. Moreover, the multiplicities of baby Verma modules in projective modules and simple modules in baby Verma modules are given. Thus we get the character formulae for simple modules and the Cartan invariants of [Formula: see text].
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24

Futorny, V. M. "Imaginary Verma Modules for Affine Lie Algebras." Canadian Mathematical Bulletin 37, no. 2 (June 1, 1994): 213–18. http://dx.doi.org/10.4153/cmb-1994-031-9.

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AbstractWe study a class of irreducible modules for Affine Lie algebras which possess weight spaces of both finite and infinite dimensions. These modules appear as the quotients of "imaginary Verma modules" induced from the "imaginary Borel subalgebra".
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25

Malikov, Fyodor. "Quantum Groups: Singular Vectors and BGG Resolution." International Journal of Modern Physics A 07, supp01b (April 1992): 623–43. http://dx.doi.org/10.1142/s0217751x92003963.

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We prove existence of BGG resolution of an irreducible highest weight module over a quantum group, classify morphisms of Verma modules over a quantum group and find formulas for singular vectors in Verma modules. As an application we find cohomology of the quantum group of the type [Formula: see text] with coefficients in a finite-dimensional module.
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26

Cai, Yan-an, Genqiang Liu, Jonathan Nilsson, and Kaiming Zhao. "Generalized Verma modules oversln+2induced fromU(hn)-freesln+1-modules." Journal of Algebra 502 (May 2018): 146–62. http://dx.doi.org/10.1016/j.jalgebra.2018.01.019.

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27

MARTINEZ-VILLA, ROBERTO. "THE HOMOGENISED ENVELOPING ALGEBRA OF THE LIE ALGEBRA sℓ(2,ℂ)." Glasgow Mathematical Journal 56, no. 3 (August 22, 2014): 551–68. http://dx.doi.org/10.1017/s0017089514000032.

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AbstractIn this paper, we study the homogenised algebra B of the enveloping algebra U of the Lie algebra sℓ(2,ℂ). We look first to connections between the category of graded left B-modules and the category of U-modules, then we prove B is Koszul and Artin–Schelter regular of global dimension four, hence its Yoneda algebra B! is self-injective of radical five zeros, and the structure of B! is given. We describe next the category of homogenised Verma modules, which correspond to the lifting to B of the usual Verma modules over U, and prove that such modules are Koszul of projective dimension two. It was proved in Martínez-Villa and Zacharia (Approximations with modules having linear resolutions, J. Algebra266(2) (2003), 671–697)] that all graded stable components of a self-injective Koszul algebra are of type ZA∞. Here, we characterise the graded B!-modules corresponding to the Koszul duality to homogenised Verma modules, and prove that these are located at the mouth of a regular component. In this way we obtain a family of components over a wild algebra indexed by ℂ.
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28

Thiel, U. "Champ: a Cherednik algebraMagmapackage." LMS Journal of Computation and Mathematics 18, no. 1 (2015): 266–307. http://dx.doi.org/10.1112/s1461157015000054.

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We present a computer algebra package based onMagmafor performing computations in rational Cherednik algebras with arbitrary parameters and in Verma modules for restricted rational Cherednik algebras. Part of this package is a new general Las Vegas algorithm for computing the head and the constituents of a module with simple head in characteristic zero, which we develop here theoretically. This algorithm is very successful when applied to Verma modules for restricted rational Cherednik algebras and it allows us to answer several questions posed by Gordon in some specific cases. We can determine the decomposition matrices of the Verma modules, the graded$G$-module structure of the simple modules, and the Calogero–Moser families of the generic restricted rational Cherednik algebra for around half of the exceptional complex reflection groups. In this way we can also confirm Martino’s conjecture for several exceptional complex reflection groups.Supplementary materials are available with this article.
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29

Cox, Ben. "Verma modules induced from nonstandard Borel subalgebras." Pacific Journal of Mathematics 165, no. 2 (October 1, 1994): 269–94. http://dx.doi.org/10.2140/pjm.1994.165.269.

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30

Jeyakumar, A. V., and P. B. Sarasija. "Socles of Verma modules in quantum groups." Bulletin of the Australian Mathematical Society 47, no. 2 (April 1993): 221–31. http://dx.doi.org/10.1017/s0004972700012466.

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In this paper the Verma modules Me(λ) over the quantum group vε(sl(n + 1), ℂ), where ε is a primitive lth root of 1 are studied. Some commutation relations among the generators of Ue are obtained. Using these relations, it is proved that the socle of Mε(λ) is non-zero.
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31

Noriyuki, Abe, and Kaneda Masaharu. "Loewy series of parabolically induced -Verma modules." Journal of the Institute of Mathematics of Jussieu 14, no. 1 (March 28, 2014): 185–220. http://dx.doi.org/10.1017/s1474748014000012.

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AbstractWe show that the modules for the Frobenius kernel of a reductive algebraic group over an algebraically closed field of positive characteristic $p$ induced from the $p$-regular blocks of its parabolic subgroups can be $\mathbb{Z}$-graded. In particular, we obtain that the modules induced from the simple modules of $p$-regular highest weights are rigid and determine their Loewy series, assuming the Lusztig conjecture on the irreducible characters for the reductive algebraic groups, which is now a theorem for large $p$. We say that a module is rigid if and only if it admits a unique filtration of minimal length with each subquotient semisimple, in which case the filtration is called the Loewy series.
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32

Cox, Ben L. "Fock Space Realizations of Imaginary Verma Modules." Algebras and Representation Theory 8, no. 2 (May 2005): 173–206. http://dx.doi.org/10.1007/s10468-005-0857-y.

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33

Vaz, Pedro. "A survey on categorification of Verma modules." Journal of Interdisciplinary Mathematics 22, no. 3 (April 3, 2019): 265–315. http://dx.doi.org/10.1080/09720502.2019.1615675.

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34

Futorny, Vyacheslay, and Iryna Kashuba. "Verma type modules for toroidal lie algebras." Communications in Algebra 27, no. 8 (January 1999): 3979–91. http://dx.doi.org/10.1080/00927879908826677.

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35

Dobrev, V. K. "Parabolic Verma Modules and Invariant Differential Operators." Physics of Particles and Nuclei 51, no. 4 (July 2020): 399–404. http://dx.doi.org/10.1134/s1063779620040231.

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36

Naisse, Grégoire, and Pedro Vaz. "An approach to categorification of Verma modules." Proceedings of the London Mathematical Society 117, no. 6 (June 21, 2018): 1181–241. http://dx.doi.org/10.1112/plms.12157.

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37

Jiang, Qifen, and Yuezhu Wu. "Verma Modules over a Block Lie Algebra." Algebra Colloquium 15, no. 02 (June 2008): 235–40. http://dx.doi.org/10.1142/s1005386708000230.

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Let [Formula: see text] be the Lie algebra with basis {Li,j, C|i, j ∈ ℤ} and relations [Li,j, Lk,l] = ((j + 1)k - i(l + 1))Li+k, j+l + iδi, -kδj+l, -2C and [C, Li,j] = 0. It is proved that an irreducible highest weight [Formula: see text]-module is quasifinite if and only if it is a proper quotient of a Verma module. An additive subgroup Γ of 𝔽 corresponds to a Lie algebra [Formula: see text] of Block type. Given a total order ≻ on Γ and a weight Λ, a Verma [Formula: see text]-module M(Λ, ≻) is defined. The irreducibility of M(Λ, ≻) is completely determined.
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38

Lü, Rencai, and Kaiming Zhao. "Verma Modules over Quantum Torus Lie Algebras." Canadian Journal of Mathematics 62, no. 2 (April 1, 2010): 382–99. http://dx.doi.org/10.4153/cjm-2010-022-1.

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AbstractRepresentations of various one-dimensional central extensions of quantum tori (called quantum torus Lie algebras) were studied by several authors. Now we define a central extension of quantum tori so that all known representations can be regarded as representations of the new quantum torus Lie algebras . The center of now is generally infinite dimensional.In this paper, Z-graded Verma modules over and their corresponding irreducible highest weight modules are defined for some linear functions . Necessary and sufficient conditions for to have all finite dimensional weight spaces are given. Also necessary and sufficient conditions for Verma modules e to be irreducible are obtained.
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39

GORDON, IAIN. "BABY VERMA MODULES FOR RATIONAL CHEREDNIK ALGEBRAS." Bulletin of the London Mathematical Society 35, no. 03 (May 2003): 321–36. http://dx.doi.org/10.1112/s0024609303001978.

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40

L'INNOCENTE, SONIA, and MIKE PREST. "RINGS OF DEFINABLE SCALARS OF VERMA MODULES." Journal of Algebra and Its Applications 06, no. 05 (October 2007): 779–87. http://dx.doi.org/10.1142/s0219498807002430.

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Let M be a Verma module over the Lie algebra, sl 2(k), of trace zero 2 × 2 matrices over the algebraically closed field k. We show that the ring, RM, of definable scalars of M is a von Neumann regular ring and that the canonical map from U( sl 2(k)) to RM is an epimorphism of rings. We also describe the Ziegler closure of M. The proofs make use of ideas from the model theory of modules.
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41

Abe, Noriyuki. "Vanishing of extensions of twisted Verma modules." Proceedings of the American Mathematical Society 137, no. 11 (November 1, 2009): 3923. http://dx.doi.org/10.1090/s0002-9939-09-09958-4.

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42

Jiang, Wei, and Wei Zhang. "Verma modules over the W(2,2) algebras." Journal of Geometry and Physics 98 (December 2015): 118–27. http://dx.doi.org/10.1016/j.geomphys.2015.07.029.

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43

Franklin, James. "Homomorphisms between Verma modules in characteristic p." Journal of Algebra 112, no. 1 (January 1988): 58–85. http://dx.doi.org/10.1016/0021-8693(88)90132-9.

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44

Cheng, Yongsheng, and Yucai Su. "Generalized Verma modules over some Block algebras." Frontiers of Mathematics in China 3, no. 1 (January 11, 2008): 37–47. http://dx.doi.org/10.1007/s11464-008-0008-y.

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45

Futorny, V. M. "Verma-type modules over affine Lie algebras." Functional Analysis and Its Applications 27, no. 3 (1993): 224–25. http://dx.doi.org/10.1007/bf01087545.

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46

Xin, Bin, and Yuezhu Wu. "Generalized Verma Modules over Lie Algebras of Weyl Type." Algebra Colloquium 16, no. 01 (March 2009): 131–42. http://dx.doi.org/10.1142/s1005386709000157.

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For a field 𝔽 of characteristic 0 and an additive subgroup Γ of 𝔽, there corresponds a Lie algebra [Formula: see text] of generalized Weyl type. Given a total order of Γ and a weight Λ, a generalized Verma [Formula: see text]-module M(Λ, ≺) is defined. In this paper, the irreducibility of M(Λ, ≺) is completely determined. It is also proved that an irreducible highest weight module over the [Formula: see text]-infinity algebra [Formula: see text] is quasifinite if and only if it is a proper quotient of a Verma module.
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47

Cantarini, Nicoletta, Fabrizio Caselli, and Victor Kac. "Classification of Degenerate Verma Modules for E(5, 10)." Communications in Mathematical Physics 385, no. 2 (March 13, 2021): 963–1005. http://dx.doi.org/10.1007/s00220-021-04031-z.

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AbstractGiven a Lie superalgebra $${\mathfrak {g}}$$ g with a subalgebra $${\mathfrak {g}}_{\ge 0}$$ g ≥ 0 , and a finite-dimensional irreducible $${\mathfrak {g}}_{\ge 0}$$ g ≥ 0 -module F, the induced $${\mathfrak {g}}$$ g -module $$M(F)={\mathcal {U}}({\mathfrak {g}})\otimes _{{\mathcal {U}}({\mathfrak {g}}_{\ge 0})}F$$ M ( F ) = U ( g ) ⊗ U ( g ≥ 0 ) F is called a finite Verma module. In the present paper we classify the non-irreducible finite Verma modules over the largest exceptional linearly compact Lie superalgebra $${\mathfrak {g}}=E(5,10)$$ g = E ( 5 , 10 ) with the subalgebra $${\mathfrak {g}}_{\ge 0}$$ g ≥ 0 of minimal codimension. This is done via classification of all singular vectors in the modules M(F). Besides known singular vectors of degree 1,2,3,4 and 5, we discover two new singular vectors, of degrees 7 and 11. We show that the corresponding morphisms of finite Verma modules of degree 1,4,7, and 11 can be arranged in an infinite number of bilateral infinite complexes, which may be viewed as “exceptional” de Rham complexes for E(5, 10).
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48

Futorny, Vyacheslav M., Alexander N. Grishkov, and Duncan J. Melville. "Verma-Type Modules for Quantum Affine Lie Algebras." Algebras and Representation Theory 8, no. 1 (March 2005): 99–125. http://dx.doi.org/10.1007/s10468-004-5765-z.

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49

Hu, Jun, Xian-Dong Wang, and Kai-Ming Zhao. "Verma modules over generalized Virasoro algebras Vir[G]." Journal of Pure and Applied Algebra 177, no. 1 (January 2003): 61–69. http://dx.doi.org/10.1016/s0022-4049(02)00173-1.

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50

Tolpygo, A. K. "A bound on the cohomologies of Verma modules." Russian Mathematical Surveys 48, no. 1 (February 28, 1993): 193–94. http://dx.doi.org/10.1070/rm1993v048n01abeh001003.

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