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Zap. Nauchn. Sem. POMI, 2015, Volume 433, Pages 20–40 (Mi znsl6125)  

This article is cited in 2 scientific papers (total in 2 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.

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English version:
Journal of Mathematical Sciences (New York), 2016, 213:5, 637–650

Bibliographic databases:

UDC: 517.9
Received: 02.03.2015
Language:

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

Citation in format AMSBIB
\Bibitem{AshMud15}
\by Th.~Ashton, A.~Mudrov
\paper Representations of quantum conjugacy classes of orthosymplectic groups
\inbook Questions of quantum field theory and statistical physics. Part~23
\serial Zap. Nauchn. Sem. POMI
\yr 2015
\vol 433
\pages 20--40
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6125}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3493678}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2016
\vol 213
\issue 5
\pages 637--650
\crossref{https://doi.org/10.1007/s10958-016-2728-y}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84957550063}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. I. Mudrov, “Regularization of Mickelsson generators for nonexceptional quantum groups”, Theoret. and Math. Phys., 192:2 (2017), 1205–1217  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    2. A. I. Mudrov, “Equivariant vector bundles over quantum projective spaces”, Theoret. and Math. Phys., 198:2 (2019), 284–295  mathnet  crossref  crossref  adsnasa  isi  elib
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