Presenting Schur superalgebras

TL;DR

This paper introduces a presentation and basis for Schur superalgebras and their quantum analogues, extending previous work on Schur algebras and utilizing weight idempotents similar to Lusztig's quantum groups.

Contribution

It provides a new presentation and basis for Schur superalgebras and their quantum versions, generalizing earlier results and incorporating Lusztig's approach.

Findings

Established a basis for Schur superalgebras and their quantum analogues.

Presented a new presentation using weight idempotents.

Extended the work of Doty and Giaquinto to superalgebras.

Abstract

We provide a presentation of the Schur superalgebra and its quantum analogue which generalizes the work of Doty and Giaquinto for Schur algebras. Our results include a basis for these algebras and a presentation using weight idempotents in the spirit of Lusztig's modified quantum groups.