University of Sydney Algebra Seminar

Anna Mkrtchyan (University of Edinburgh/University of Bonn)

Friday 21 September, 3-4pm, Place: Carslaw 375

Gradings on the Brauer algebra

Brauer algebras B_n(\delta) are finite dimensional algebras introduced by Richard Brauer in order to study the n-th tensor power of the defining representations of the orthogonal and symplectic groups. They play the same role that the group algebras of the symmetric groups do for the representation theory of the general linear groups in the classical Schur-Weyl duality. We will discuss two different constructions which show that the Brauer algebras are graded cellular algebras and then show that they define the same gradings on B_n(\delta).