On the Quasi-Heredity of Birman–Wenzl Algebras

Abstract

In this paper we consider the Birman Wenzl algebras over an arbitrary field and prove that they are cellular in the sense of Graham and Lehrer. Furthermore, we determine for which parameters the Birman Wenzl algebras are quasi-hereditary. So the general theory of cellular algebras and quasi-hereditary algebras applies to Birman Wenzl algebras. As a consequence, we can determine all irreducible representations of the Birman Wenzl algebras by linear algebra methods. We prove also that the new Hecke algebras induced from Birman Wenzl algebras are Frobenius over a field (but not always cellular). Academic Press

Specht modules and semisimplicity criteria for Brauer and Birman–Murakami–Wenzl algebras

“…. , n}, depending as n is odd or even, the order ☎ as defined above is compatible with a cellular structure of the Birman-Murakami-Wenzl and Brauer algebras, as shown in [4], [5] and [13].…”

Cellular Bases for Algebras with a Jones Basic Construction

“…The version of the presentation given here follows [31]. Cellularity of the BMW algebras was established in [8,9,43]. Morton and Wassermann [31] give a realization of the BMW algebra as an algebra of (n, n)-tangle diagrams modulo regular isotopy and the following Kauffman skein relations:…”

Decomposition matrices of Birman–Murakami–Wenzl algebras

“…If λ ′ is e-restricted, then λ is called e-regular. It is proved in [30] that D f,λ = 0 if and only if λ is e-restricted and f = r/2 if r is even and ̺ 2 = 1. By Theorem 4.2(2), similar result holds forD f,λ .…”