University of Sydney Algebra Seminar

Armin Shalile (Universitat Stuttgart)

Friday 14th February, 12:05-12:55pm, Carslaw 350

Decomposition numbers of Brauer algebras via Jucys-Murphy elements

Brauer algebras were introduced by Richard Brauer in 1937 and are closely related to the representation theory of orthogonal, symplectic and symmetric groups. They are also a prototypical example of a cellular algebra in the sense of Graham and Lehrer. In this talk, we will give a description of decomposition numbers of Brauer algebras over a field of characteristic not dividing the degree of the Brauer algebra. The description will be in terms of the action of a family of distinguished elements of the algebra, the so-called Jucys-Murphy elements. This is motivated by the Okounkov-Vershik approach to the study of symmetric groups which proposes to view the algebra generated by Jucys-Murphy elements as a Cartan subalgebra and study the representation theory in the spirit of Lie theory.