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

Abstract

In memory of J.A. Green, with the highest admiration. AbstractWe 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 the quantised Borel-Schur algebra S − α,β (n, r).

Decreasing diagrams and coherent presentations

“…Using this sufficient condition we establish a coherent presentation of the 0-Hecke monoid. This presentation was used in the joint work of the author with A. P. Santana [5] to exhibit an action of the 0-Hecke monoid on the category of rational modules for the quantum Borel group. Note that our coherent presentation contains the coherent presentation of the braid group obtained by Guiraud et al in [2].…”