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Korean Mathematical Society JKMS

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J. Korean Math. Soc. 2023; 60(6): 1255-1302

Online first article October 25, 2023      Printed November 1, 2023

https://doi.org/10.4134/JKMS.j230020

Copyright © The Korean Mathematical Society.

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

Helena Jonsson, Volodymyr Mazorchuk, Elin Persson Westin, Shraddha Srivastava, Mateusz Stroinski, Xiaoyu Zhu

Uppsala University; Uppsala University; Uppsala University; Indian Institute of Technology; Uppsala University; Ningbo University

Abstract

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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 $\mathcal{O}$.

Keywords: Singular Artin monoids, desingularization map, BGG category $\mathcal{O}$, projective functors

MSC numbers: Primary 17B10, 20F36, 20M05

Supported by: This research is partially supported by the Swedish Research Council.

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