A Poset Connected to Artin Monoids of Simply Laced Type

2005/02/24 by A. M. Cohen, Arjeh M. Cohen, Cohen, A. M. +5
Mathematics · #16G10(Secondary) #20F36 (Primary) #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Representation Theory (math.RT) #math.GR #math.RT #msc:20F36

paper · pdf · doi:10.48550/arxiv.math/0502501

arxiv created 2005/02/24 · openalex publication_date 2005/02/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let W be a Weyl group whose type is a simply laced Dynkin diagram. On several W-orbits of sets of mutually commuting reflections, a poset is described which plays a role in linear representatons of the corresponding Artin group A. The poset generalizes many properties of the usual order on positive roots of W given by height. In this paper, a linear representation of the positive monoid of A is defined by use of the poset.

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