Reducing Rouquier complexes
type: Item
instance of: scholarly article
title: Reducing Rouquier complexes
author: Leonardo Maltoni
published in: Proceedings of the London Mathematical Society. Third Series
publication date: 2024-08-01T00:00:00Z
review text: Rouquier complexes, introduced in [\textit{R. Rouquier}, Contemp. Math. 406, 137--167 (2006; Zbl 1162.20301)], are certain complexes defined in the homotopy category of the Hecke category. These complexes define a strong categorical action of the generalised braid group (also known as Artin-Tits group) \(B_W\) associated to the Coxeter system \((W,S)\), which is conjecturally faithful. They are important as many categorical actions of \(B_W\) can be studied as their quotient, and they can also be used to construct a triply-graded link homology via the work of \textit{M. Khovanov} [Int. J. Math. 18, No. 8, 869--885 (2007; Zbl 1124.57003)].\N\NThis paper provides an explicit description of the minimal representatives of these complexes, namely the homotopy equivalent complexes that have no contractible summand (no more Gaussian elimination can be applied). The main tool comes from an algebraic description of (discrete) Morse theory studied in [\textit{E. Sköldberg}, Trans. Am. Math. Soc. 358, No. 1, 115--129 (2006; Zbl 1150.16008)]. The minimal complexes are defined in terms of contraction of monotonous subwords, which can be found in \S 3.6.
reviewed by: Edmund Heng
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 20C08
Mathematics Subject Classification ID: 13P20
Mathematics Subject Classification ID: 20F36
Mathematics Subject Classification ID: 18N25
zbMATH DE Number: 7890760
zbMATH Keywords: Hecke category
zbMATH Keywords: Rouquier complexes
zbMATH Keywords: discrete Morse theory
zbMATH Keywords: Gaussian elimination
zbMATH Keywords: Artin groups
MaRDI profile type: Publication
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DOI: 10.1112/PLMS.12617
description: scientific article; zbMATH DE number 7890760