On the Jucys-Murphy method and fusion procedure for the Sergeev superalgebra

Abstract

We use the Jucys-Murphy elements to construct a complete set of primitive idempotents for the Sergeev superalgebra ${\mathcal{S}}_n$. We produce seminormal forms for the simple modules over ${\mathcal{S}}_n$ and over the spin symmetric group algebra with explicit constructions of basis vectors. We show that the idempotents can also be obtained from a new version of the fusion procedure.

24 pages, seminormal form for the spin symmetric group algebra added