The cyclotomic BMW algebra associated with the two string type B braid group

TL;DR

This paper studies the cyclotomic BMW algebra for n=2, providing a basis and constructing its left regular representation, thereby extending understanding of these algebraic structures related to braid groups.

Contribution

It introduces a basis for B_2^k and constructs its left regular representation, advancing the algebraic understanding of cyclotomic BMW algebras for the two-string case.

Findings

Established a basis for B_2^k

Constructed the left regular representation

Extended algebraic understanding of cyclotomic BMW algebras

Abstract

The cyclotomic Birman-Murakami-Wenzl (or BMW) algebras B_n^k, introduced by R. Haring-Oldenburg, are extensions of the cyclotomic Hecke algebras of Ariki-Koike, in the same way as the BMW algebras are extensions of the Hecke algebras of type A. In this paper we focus on the case n=2, producing a basis of B_2^k and constructing its left regular representation.