Irreducible representations of q-Schur superalgebras at a root of unity

TL;DR

This paper classifies all irreducible modules of q-Schur superalgebras at roots of unity, providing a comprehensive understanding of their representation theory in characteristic zero.

Contribution

It offers the first complete classification of irreducible modules for q-Schur superalgebras at roots of unity under specified conditions.

Findings

Complete classification of irreducible modules achieved

Results applicable when q is an odd-order primitive root of unity

Advances understanding of q-Schur superalgebra representations

Abstract

Under the assumption that the quantum parameter $q$ is an $l$-th primitive root of unity with $l$ odd in a field $F$ of characteristic 0 and $m+n\geq r$, we obtained a complete classification of irreducible modules of the $q$-Schur superalgebra introduced H. Rui and the first Author.