Blocks of Birman-Murakami-Wenzl Algebras

Abstract

Birman, Wenzl [3], and independently Murakami [19] introduced a class of finite dimensional algebras , which are known as the Birman–Murakami–Wenzl algebras or BMW algebras. When the ground field κ contains invertible r and q such that o(q 2 ), the multiplicative order of q 2 , is strictly greater than n, and char(κ), the characteristic of κ is not 2, we determine the structure of the cell module Δ(1, λ) of , where λ is any partition of n −2. In particular, we compute the dimension of the simple head of Δ(1, λ). Cox, De Visscher, and Martin have classified the blocks of Brauer algebras B n in characteristic zero [5]. We solve the similar problem for over the aforementioned field κ. As a by-product, we give a criterion for each module of being equal to its simple head over an arbitrary field.