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

TL;DR

This paper develops new methods using Jucys-Murphy elements and fusion procedures to explicitly construct primitive idempotents and seminormal forms for the Sergeev superalgebra and related modules.

Contribution

It introduces a novel fusion procedure and explicit seminormal forms for simple modules of the Sergeev superalgebra, advancing representation theory techniques.

Findings

Complete set of primitive idempotents constructed

Explicit seminormal forms for simple modules provided

Idempotents derived from a new fusion procedure

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.