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Journal articles on the topic 'Calogero-Moser spaces'

Author: Grafiati

Published: 5 October 2024

Last updated: 31 July 2025

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1

Bellamy, Gwyn. "On singular Calogero-Moser spaces." Bulletin of the London Mathematical Society 41, no. 2 (2009): 315–26. http://dx.doi.org/10.1112/blms/bdp019.

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2

BEREST, YURI, ALIMJON ESHMATOV, and FARKHOD ESHMATOV. "MULTITRANSITIVITY OF CALOGERO-MOSER SPACES." Transformation Groups 21, no. 1 (2015): 35–50. http://dx.doi.org/10.1007/s00031-015-9332-y.

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3

Ben-Zvi, David, and Thomas Nevins. "Perverse bundles and Calogero–Moser spaces." Compositio Mathematica 144, no. 6 (2008): 1403–28. http://dx.doi.org/10.1112/s0010437x0800359x.

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AbstractWe present a simple description of moduli spaces of torsion-free 𝒟-modules (𝒟-bundles) on general smooth complex curves, generalizing the identification of the space of ideals in the Weyl algebra with Calogero–Moser quiver varieties. Namely, we show that the moduli of 𝒟-bundles form twisted cotangent bundles to moduli of torsion sheaves on X, answering a question of Ginzburg. The corresponding (untwisted) cotangent bundles are identified with moduli of perverse vector bundles on T*X, which contain as open subsets the moduli of framed torsion-free sheaves (the Hilbert schemes T*X[n] in

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4

Berest, Yuri. "Calogero–Moser spaces over algebraic curves." Selecta Mathematica 14, no. 3-4 (2009): 373–96. http://dx.doi.org/10.1007/s00029-009-0518-9.

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5

Kuyumzhiyan, Karine. "Infinite transitivity for Calogero-Moser spaces." Proceedings of the American Mathematical Society 148, no. 9 (2020): 3723–31. http://dx.doi.org/10.1090/proc/15030.

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6

Bellamy, Gwyn. "Factorization in generalized Calogero–Moser spaces." Journal of Algebra 321, no. 1 (2009): 338–44. http://dx.doi.org/10.1016/j.jalgebra.2008.09.015.

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7

Andrist, Rafael. "The density property for Calogero–Moser spaces." Proceedings of the American Mathematical Society 149, no. 10 (2021): 4207–18. http://dx.doi.org/10.1090/proc/15457.

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We prove the algebraic density property for the Calogero–Moser spaces C n {\mathcal {C}_{n}} , and give a description of the identity component of the group of holomorphic automorphisms of C n {\mathcal {C}_{n}} .

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8

HAINE, LUC, EMIL HOROZOV, and PLAMEN ILIEV. "TRIGONOMETRIC DARBOUX TRANSFORMATIONS AND CALOGERO–MOSER MATRICES." Glasgow Mathematical Journal 51, A (2009): 95–106. http://dx.doi.org/10.1017/s0017089508004813.

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AbstractWe characterize in terms of Darboux transformations the spaces in the Segal–Wilson rational Grassmannian, which lead to commutative rings of differential operators having coefficients which are rational functions of ex. The resulting subgrassmannian is parametrized in terms of trigonometric Calogero–Moser matrices.

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9

Oblomkov, Alexei. "Double affine Hecke algebras and Calogero-Moser spaces." Representation Theory of the American Mathematical Society 8, no. 10 (2004): 243–66. http://dx.doi.org/10.1090/s1088-4165-04-00246-8.

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10

Horozov, Emil. "Calogero-Moser spaces and an adelic $W$-algebra." Annales de l’institut Fourier 55, no. 6 (2005): 2069–90. http://dx.doi.org/10.5802/aif.2152.

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11

Bellamy, Gwyn, and Victor Ginzburg. "SL2-action on Hilbert Schemes and Calogero-Moser spaces." Michigan Mathematical Journal 66, no. 3 (2017): 519–32. http://dx.doi.org/10.1307/mmj/1496995337.

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12

Eshmatov, Farkhod, Alimjon Eshmatov, and Yuri Berest. "On subgroups of the Dixmier group and Calogero-Moser spaces." Electronic Research Announcements in Mathematical Sciences 18 (March 2011): 12–21. http://dx.doi.org/10.3934/era.2011.18.12.

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13

Chabaud, Ulysse, and Saeed Mehraban. "Holomorphic representation of quantum computations." Quantum 6 (October 6, 2022): 831. http://dx.doi.org/10.22331/q-2022-10-06-831.

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We study bosonic quantum computations using the Segal-Bargmann representation of quantum states. We argue that this holomorphic representation is a natural one which not only gives a canonical description of bosonic quantum computing using basic elements of complex analysis but also provides a unifying picture which delineates the boundary between discrete- and continuous-variable quantum information theory. Using this representation, we show that the evolution of a single bosonic mode under a Gaussian Hamiltonian can be described as an integrable dynamical system of classical Calogero-Moser p

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14

Przeździecki, Tomasz. "The combinatorics of C⁎-fixed points in generalized Calogero-Moser spaces and Hilbert schemes." Journal of Algebra 556 (August 2020): 936–92. http://dx.doi.org/10.1016/j.jalgebra.2020.04.003.

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15

Kesten, J., S. Mathers, and Z. Normatov. "Infinite transitivity on the Calogero-Moser space C2." Algebra and Discrete Mathematics 31, no. 2 (2021): 227–50. http://dx.doi.org/10.12958/adm1656.

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We prove a particular case of the conjecture of Berest--Eshmatov--Eshmatov by showing that the group of unimodular automorphisms of C[x,y] acts in an infinitely-transitive way on the Calogero-Moser space C2.

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16

Prykarpatski, Anatolij K. "Quantum Current Algebra in Action: Linearization, Integrability of Classical and Factorization of Quantum Nonlinear Dynamical Systems." Universe 8, no. 5 (2022): 288. http://dx.doi.org/10.3390/universe8050288.

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This review is devoted to the universal algebraic and geometric properties of the non-relativistic quantum current algebra symmetry and to their representations subject to applications in describing geometrical and analytical properties of quantum and classical integrable Hamiltonian systems of theoretical and mathematical physics. The Fock space, the non-relativistic quantum current algebra symmetry and its cyclic representations on separable Hilbert spaces are reviewed and described in detail. The unitary current algebra family of operators and generating functional equations are described.

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17

BONNAFÉ, CÉDRIC. "AUTOMORPHISMS AND SYMPLECTIC LEAVES OF CALOGERO–MOSER SPACES." Journal of the Australian Mathematical Society, October 17, 2022, 1–32. http://dx.doi.org/10.1017/s1446788722000180.

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Abstract We study the symplectic leaves of the subvariety of fixed points of an automorphism of a Calogero–Moser space induced by an element of finite order of the normalizer of the associated complex reflection group. We give a parametrization à la Harish-Chandra of its symplectic leaves (generalizing earlier works of Bellamy and Losev). This result is inspired by the mysterious relations between the geometry of Calogero–Moser spaces and unipotent representations of finite reductive groups, which is the theme of another paper, C. Bonnafé [‘Calogero–Moser spaces vs unipotent representations’,

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18

Bonnafé, Cédric, and Ulrich Thiel. "Computational aspects of Calogero–Moser spaces." Selecta Mathematica 29, no. 5 (2023). http://dx.doi.org/10.1007/s00029-023-00878-3.

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AbstractWe present a series of algorithms for computing geometric and representation-theoretic invariants of Calogero–Moser spaces and rational Cherednik algebras associated with complex reflection groups. In particular, we are concerned with Calogero–Moser families (which correspond to the $$\mathbb {C}^\times $$ C × -fixed points of the Calogero–Moser space) and cellular characters (a proposed generalization by Rouquier and the first author of Lusztig’s constructible characters based on a Galois covering of the Calogero–Moser space). To compute the former, we devised an algorithm for determi

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19

Normatov, Zafar, Yingqi Wang, and Shuai Zeng. "On trigonometric Calogero-Moser spaces." Journal of Geometry and Physics, April 2025, 105515. https://doi.org/10.1016/j.geomphys.2025.105515.

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20

"Calogero-Moser spaces vs unipotent representations." Pure and Applied Mathematics Quarterly 21, no. 1 (2024): 131–200. https://doi.org/10.4310/pamq.241203032151.

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21

Berest, Yuri, and Oleg Chalykh. "A∞-modules and Calogero-Moser spaces." Journal für die reine und angewandte Mathematik (Crelles Journal) 2007, no. 607 (2007). http://dx.doi.org/10.1515/crelle.2007.046.

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22

Bonnafé, Cédric, and Ruslan Maksimau. "Fixed points in smooth Calogero–Moser spaces." Annales de l'Institut Fourier, June 7, 2021, 1–36. http://dx.doi.org/10.5802/aif.3404.

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23

Bonnafé, Cédric, and Peng Shan. "On the Cohomology of Calogero–Moser Spaces." International Mathematics Research Notices, March 28, 2018. http://dx.doi.org/10.1093/imrn/rny036.

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24

Andrist, Rafael B., and Gaofeng Huang. "The symplectic density property for Calogero–Moser spaces." Journal of the London Mathematical Society 111, no. 2 (2025). https://doi.org/10.1112/jlms.70100.

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AbstractWe introduce the symplectic density property and the Hamiltonian density property together with the corresponding versions of Andersén–Lempert theory. We establish these properties for the Calogero–Moser space of particles and describe its group of holomorphic symplectic automorphisms.

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25

Hu, Sen, Andrey Losev, and Dongheng Ye. "QFT on fuzzy disc and Calogero–Moser phase space." Modern Physics Letters A, February 26, 2025. https://doi.org/10.1142/s0217732324502298.

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Noncommutative spaces with boundaries are expected to play an important role in connection between Feynman and functorial definitions of quantum field theory. Since actions of all field theories may be written in terms of De Rham algebra, the crucial step is to construct it on such noncommutative spaces. Here, we do it for the fuzzy disc. In our construction, we had to include new degrees of freedom associated to boundary. Surprisingly, the noncommutative analogue of the moduli space of flat connections turns out to be a phase space of Calogero–Moser system. We proceed by construction of nonco

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26

Voit, Michael. "Freezing limits for Calogero–Moser–Sutherland particle models." Studies in Applied Mathematics, August 4, 2023. http://dx.doi.org/10.1111/sapm.12628.

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AbstractOne‐dimensional interacting particle models of Calogero–Moser–Sutherland type with N particles can be regarded as diffusion processes on suitable subsets of like Weyl chambers and alcoves with second‐order differential operators as generators of the transition semigroups, where these operators are singular on the boundaries of the state spaces. The most relevant examples are multivariate Bessel processes and Heckman–Opdam processes in a compact and noncompact setting where in all cases, these processes are related to special functions associated with root systems. More precisely, the t

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27

Normatov, Zafar, and Rustam Turdibaev. "Calogero-Moser Spaces and the Invariants of Two Matrices of Degree 3." Transformation Groups, October 18, 2022. http://dx.doi.org/10.1007/s00031-022-09776-y.

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28

Berntson, Bjorn K., Ernest G. Kalnins, and Willard Miller. "Toward Classification of 2nd Order Superintegrable Systems in 3-Dimensional Conformally Flat Spaces with Functionally Linearly Dependent Symmetry Operators." Symmetry, Integrability and Geometry: Methods and Applications, December 16, 2020. http://dx.doi.org/10.3842/sigma.2020.135.

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We make significant progress toward the classification of 2nd order superintegrable systems on 3-dimensional conformally flat space that have functionally linearly dependent (FLD) symmetry generators, with special emphasis on complex Euclidean space. The symmetries for these systems are linearly dependent only when the coefficients are allowed to depend on the spatial coordinates. The Calogero-Moser system with 3 bodies on a line and 2-parameter rational potential is the best known example of an FLD superintegrable system. We work out the structure theory for these FLD systems on 3D conformall

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29

Eshmatov, Farkhod, Xabier García-Martínez, Zafar Normatov, and Rustam Turdibaev. "On the Coordinate Rings of Calogero-Moser Spaces and the Invariant Commuting Variety of a Pair of Matrices." Results in Mathematics 80, no. 3 (2025). https://doi.org/10.1007/s00025-025-02385-7.

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