School of Mathematics and Statistics
Algebra Seminar
The University of Sydney

University of Sydney Algebra Seminar


Hebing Rui (East China Normal University)

Friday 30th March, 12.05-12.55pm, Carslaw 375

Discriminants of Brauer algebras

Brauer algebras were introduced by Richard Brauer in order to study the tensor representations of the defining space for orthogonal or symplectic groups. In 1995, Graham and Lehrer proved that Brauer algebras over a commutative ring are cellular algebras. A natural question is how to compute the Gram determinant for each cell module of a Brauer algebra. In this talk, I will answer this question by giving a recursive formula. Such a formula has been generalized to Birman-Wenzl algebras, the q-analogue of Brauer algebras. We also give necessary and sufficient conditions for the semisimplicity of Birman-Wenzl algebras over an arbitrary field, which improves work by H. Wenzl in 1990.

This is joint work with Mei Si.