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Quantum symmetric conjugacy classes of non-exceptional groups

Dakhilallah Algethami, Andrey Mudrov

Abstract

We evaluate one-dimensional representations of quantum symmetric conjugacy classes of classical matrix groups along with their quantum stabilizer subgroups.

Quantum symmetric conjugacy classes of non-exceptional groups

Abstract

We evaluate one-dimensional representations of quantum symmetric conjugacy classes of classical matrix groups along with their quantum stabilizer subgroups.
Paper Structure (11 sections, 8 theorems, 83 equations)

This paper contains 11 sections, 8 theorems, 83 equations.

Table of Contents

  1. Introduction
  2. Basics of quantum groups
  3. Points in quantum symmetric conjugacy classes
  4. Symmetric conjugacy classes and their quantization
  5. Quasi-classical limit of reflection equation
  6. Left coideal subalgebra $U_q(\mathfrak{k})\subset U_q(\mathfrak{g})$
  7. $U_q(\mathfrak{k})$ as a quantum isotropy subgroup
  8. $\mathfrak{k}=\mathfrak{s}\mathfrak{l}(n+1)$
  9. $\mathfrak{k}=\mathfrak{s}\mathfrak{o}(2n+1)$
  10. $\mathfrak{k}=\mathfrak{s}\mathfrak{p}(2n)$
  11. $\mathfrak{k}=\mathfrak{s}\mathfrak{o}(2n)$

Key Result

Lemma 3.1

The bivector field $\varphi=\omega^{l,r}-\omega^{r,l}\in \wedge^2 T(G)$ is invariant.

Theorems & Definitions (17)

  • Lemma 3.1
  • proof
  • Lemma 3.2
  • proof
  • Proposition 3.3
  • proof
  • Definition 3.4
  • Theorem 3.5
  • proof
  • Proposition 3.6
  • ...and 7 more