English

Enhanced Brauer algebras and enhanced dualities for orthogonal and symplectic groups

Representation Theory 2021-11-17 v1

Abstract

This note is a sequel to Shu-Xue-Yao's paper \cite{BYY} where the author studied the so-called enhanced groups and related dualities for type AA. In this note, we continue to investigate the enhanced dualities for classical groups of type BB, CC, and DD. To show this, we first introduce an enhanced Brauer algebra. Due to Proposition \ref{B dual}, we can easily obtain the restricted and Levi dualities, hence the parabolic duality is naturally described. Moreover, a special case is listed in \S\ref{3} by some explicit calculations.

Keywords

Cite

@article{arxiv.2111.08287,
  title  = {Enhanced Brauer algebras and enhanced dualities for orthogonal and symplectic groups},
  author = {Bin Liu},
  journal= {arXiv preprint arXiv:2111.08287},
  year   = {2021}
}