On the quasi-heredity of Birman-Wenzl algebras

摘要

In this paper we consider the Birman Wenzl algebras over on 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 linens algebra methods. We prove also that the new Hecke algebras induced from Birman-Wenzl algebras are Frobenius over a field (but not always cellular). (C) 2000 Academic Press. [References: 21]