Home Brauer algebras of type B
Article
Licensed
Unlicensed Requires Authentication

Brauer algebras of type B

  • Arjeh M. Cohen EMAIL logo and Shoumin Liu
Published/Copyright: March 22, 2013

Abstract

For each n ≥ 1, we define an algebra having many properties that one might expect to hold for a Brauer algebra of type Bn. It is defined by means of a presentation by generators and relations. We show that this algebra is a subalgebra of the Brauer algebra of type Dn+1 and point out a cellular structure in it. This work is a natural sequel to the introduction of Brauer algebras of type Cn, which are subalgebras of classical Brauer algebras of type A2n-1 and differ from the current ones for n > 2. A novel feature is the failure of admissible root sets to describe the tops and bottoms of the diagrams corresponding to monomials in the Brauer algebra of type Bn; instead of these sets we use extended admissible sets in order to find normal forms for monomials in the algebra.

We would like to thank David Wales for his interest, help, and improvements to this paper, and the anonymous referee for his/her criticism on the first version, which led to a much better exposition of the results.

Received: 2012-3-31
Revised: 2012-12-19
Published Online: 2013-3-22
Published in Print: 2015-3-1

© 2015 by De Gruyter

Downloaded on 3.11.2025 from https://www.degruyterbrill.com/document/doi/10.1515/forum-2012-0041/html
Scroll to top button