The BMW Algebras of Type Dn

Lecturer: David Wales

I will outline joint work with Arjeh Cohen and Dié Gijsbers in which we have found the exact dimensions of the BMW algebras of type Dn. In earlier work we had conjectured these dimensions. We use a connection to the Brauer algebras of these types and in particular to certain kinds of rewrite rules for these. These are done in such a way that we are able to lift them to the BMW algebras using induction. In particular a lift of a basis for the Brauer algebras becomes a basis for the BMW algebras. We are able to find the dimension of the Brauer algebras using some diagrams connected to them. The rewrite rules seem new even for the classical Brauer algebras of type An-1.

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