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Proof of Cellini’s conjecture on self-avoiding paths in Coxeter groups

Part of: Special aspects of infinite or finite groups Representation theory of groups

Published online by Cambridge University Press:  30 November 2011

Matthew Dyer
Matthew Dyer*
Affiliation:
Department of Mathematics, 255 Hurley Building, University of Notre Dame, Notre Dame, Indiana 46556, USA (email: dyer.1@nd.edu)
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Abstract

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This note proves Cellini’s conjecture that, in a Coxeter system (W,S) with reflections T, the T-increasing paths in W are self-avoiding. Here, a T-increasing path is a sequence v,t1v,…,tn⋯t1v in W with ti∈T and t1≺⋯≺tn in a reflection order ⪯ of T.

Keywords

Coxeter grouproot systemHecke algebraBruhat order

MSC classification

Secondary: 20F55: Reflection and Coxeter groups 20C08: Hecke algebras and their representations

Information

Type
Research Article
Information
Compositio Mathematica , Volume 148 , Issue 2 , March 2012 , pp. 548 - 554
Copyright
Copyright © Foundation Compositio Mathematica 2011

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