Finite quotients of singular Artin monoids and categorification of the desingularization map

TL;DR

This paper explores the structure and representation theory of singular Artin monoids, introduces generalizations of the desingularization map, and provides a categorification using BGG category O, advancing understanding of their algebraic and categorical properties.

Contribution

It presents a categorification of the desingularization map for singular Artin monoids related to finite Weyl groups via BGG category O, and offers explicit presentations of finite quotient monoids.

Findings

Categorification of the desingularization map achieved.

Explicit presentations for finite quotient monoids provided.

Enhanced understanding of the structure and representations of singular Artin monoids.

Abstract

We study various aspects of the structure and representation theory of singular Artin monoids. This includes a number of generalizations of the desingularization map and explicit presentations for certain finite quotient monoids of diagrammatic nature. The main result is a categorification of the classical desingularization map for singular Artin monoids associated to finite Weyl groups using BGG category $\mathcal{O}$.