Kevin Coulembier (U Sydney)

The periplectic Brauer algebra.

Abstract:

An analogue of the Brauer algebra was introduced by Moon to study invariant theory for the periplectic Lie superalgebra. This algebra is not cellular in the sense of Graham and Lehrer, but has an interesting structure of a standardly based algebra, in the sense of Du and Rui. Starting from this structure we derive the Cartan decomposition matrix and study cohomology (including construction of quasi-hereditary 1-covers) for this algebra. As an application we obtain the block decomposition of the category of integrable modules over the periplectic Lie supergroup.