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Zapiski Nauchnykh Seminarov POMI, 2015, Volume 433, Pages 20–40
(Mi znsl6125)
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This article is cited in 4 scientific papers (total in 4 papers)
Representations of quantum conjugacy classes of orthosymplectic groups
Th. Ashton, A. Mudrov Department of Mathematics, University of Leicester, University Road, LE1 7RH Leicester, UK
Abstract:
Let $G$ be the complex symplectic or special orthogonal group and $\mathfrak g$ its Lie algebra. With every point $x$ of the maximal torus $T\subset G$ we associate a highest weight module $M_x$ over the Drinfeld–Jimbo quantum group $U_q(\mathfrak g)$ and a quantization of the conjugacy class of $x$ by operators in $\mathrm{End}(M_x)$. These quantizations are isomorphic for $x$ lying on the same orbit of the Weyl group, and $M_x$ support different representations of the same quantum conjugacy class.
Key words and phrases:
quantum groups, deformation quantization, conjugacy classes.
Received: 02.03.2015
Citation:
Th. Ashton, A. Mudrov, “Representations of quantum conjugacy classes of orthosymplectic groups”, Questions of quantum field theory and statistical physics. Part 23, Zap. Nauchn. Sem. POMI, 433, POMI, St. Petersburg, 2015, 20–40; J. Math. Sci. (N. Y.), 213:5 (2016), 637–650
Linking options:
https://www.mathnet.ru/eng/znsl6125 https://www.mathnet.ru/eng/znsl/v433/p20
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Abstract page: | 214 | Full-text PDF : | 31 | References: | 47 |
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