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 . In this note, we continue to investigate the enhanced dualities for classical groups of type , , and . 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}
}