An action of the Hecke monoid on rational modules for the Borel subgroup of a quantised general linear group

TL;DR

This paper constructs a Hecke monoid action on rational modules for the quantum Borel subgroup of a quantum general linear group, revealing new symmetries and structures in quantum algebra representations.

Contribution

It introduces a novel Hecke monoid action on categories of rational and polynomial modules for quantum Borel subgroups, extending understanding of quantum group representations.

Findings

Hecke monoid acts on rational modules for quantum Borel subgroup

Action restricts to polynomial modules for the quantum subgroup

Induces an action on modules for quantised Borel-Schur algebras

Abstract

We construct an action of the Hecke monoid on the category of rational modules for the quantum negative Borel subgroup of the quantum general linear group. We also show that this action restricts to the category of polynomial modules for this quantum subgroup and induces an action on the category of modules for quantised Borel-Schur algebras.