Seminormal bases of cyclotomic Hecke-Clifford algebras

TL;DR

This paper constructs seminormal bases and primitive idempotents for semisimple cyclotomic Hecke-Clifford superalgebras, providing explicit descriptions of module actions and algebra structures.

Contribution

It introduces explicit seminormal bases and primitive idempotents for these superalgebras, enhancing understanding of their module theory.

Findings

Explicit seminormal bases constructed

Primitive idempotents explicitly described

Actions of generators on bases clarified

Abstract

In this paper, we describe actions of standard generators on certain bases of simple modules for semisimple cyclotomic Hecke-Clifford superalgebras. As applications, we explicitly construct a complete set of primitive idempotents and seminormal bases for these algebras.