Compact Schur-Weyl duality: Real Lie groups and the cyclotomic Brauer algebra

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Abstract

We show that the centraliser of the maximal compact subgroup of the real groups O(p,q) and Sp 2n(R) acting on tensors of their standard representation is isomorphic to the level 2 cyclotomic Brauer algebra with certain parameters in C. We also prove that for Sp 2n(R) this cyclotomic Brauer algebra is Morita equivalent to a direct sum of walled Brauer algebras.

Original languageEnglish
Article number107082
JournalJ. Pure Appl. Algebra
Volume226
Issue number11
DOIs
Publication statusPublished - 15 Mar 2022

Keywords

  • Brauer algebra
  • Lie algebra
  • Real Lie group
  • Schur-Weyl duality

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