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Quantum Conjugacy Classes of Simple Matrix Groups

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Abstract

Let G be a simple complex classical group and \(\mathfrak{g}\) its Lie algebra. Let \(\mathcal{U}_\hbar(\mathfrak{g})\) be the Drinfeld-Jimbo quantization of the universal enveloping algebra \(\mathcal{U}(\mathfrak{g})\). We construct an explicit \(\mathcal{U}_\hbar(\mathfrak{g})\)-equivariant quantization of conjugacy classes of G with Levi subgroups as the stabilizers.

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Authors and Affiliations

  1. Department of Mathematics, University of York, York, YO10 5DD, UK

    A. Mudrov

  2. St. Petersburg Department of Steklov Mathematical Institute, Fontanka 27, 191011, St. Petersburg, Russia

    A. Mudrov

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  1. A. Mudrov
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Correspondence to A. Mudrov.

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Communicated by L. Takhtajan

Dedicated to the memory of Joseph Donin

This research is partially supported by the Emmy Noether Research Institute for Mathematics, the Minerva Foundation of Germany, the Excellency Center “Group Theoretic Methods in the study of Algebraic Varieties” of the Israel Science foundation, by the EPSRC grant C511166, and by the RFBR grant no. 06-01-00451.

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Mudrov, A. Quantum Conjugacy Classes of Simple Matrix Groups. Commun. Math. Phys. 272, 635–660 (2007). https://doi.org/10.1007/s00220-007-0222-6

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