Intrinsic reflections in Coxeter systems

Bernhard Mühlherr; Koji Nuida

doi:10.1016/j.jcta.2016.06.009

Intrinsic reflections in Coxeter systems

Bernhard Mühlherr, Koji Nuida

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

Let (W,S) be a Coxeter system and let s∈S. We call s a right-angled generator of (W,S) if st=ts or st has infinite order for each t∈S. We call s an intrinsic reflection of W if s∈R^W for all Coxeter generating sets R of W. We give necessary and sufficient conditions for a right-angled generator s∈S of (W,S) to be an intrinsic reflection of W.

Original language	English
Pages (from-to)	326-360
Number of pages	35
Journal	Journal of Combinatorial Theory. Series A
Volume	144
DOIs	https://doi.org/10.1016/j.jcta.2016.06.009
Publication status	Published - Nov 1 2016
Externally published	Yes

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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10.1016/j.jcta.2016.06.009

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title = "Intrinsic reflections in Coxeter systems",

abstract = "Let (W,S) be a Coxeter system and let s∈S. We call s a right-angled generator of (W,S) if st=ts or st has infinite order for each t∈S. We call s an intrinsic reflection of W if s∈RW for all Coxeter generating sets R of W. We give necessary and sufficient conditions for a right-angled generator s∈S of (W,S) to be an intrinsic reflection of W.",

keywords = "Coxeter groups, Isomorphism problem, Reflections",

author = "Bernhard M{\"u}hlherr and Koji Nuida",

note = "Publisher Copyright: {\textcopyright} 2016 Elsevier Inc.",

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doi = "10.1016/j.jcta.2016.06.009",

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AU - Mühlherr, Bernhard

AU - Nuida, Koji

PY - 2016/11/1

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N2 - Let (W,S) be a Coxeter system and let s∈S. We call s a right-angled generator of (W,S) if st=ts or st has infinite order for each t∈S. We call s an intrinsic reflection of W if s∈RW for all Coxeter generating sets R of W. We give necessary and sufficient conditions for a right-angled generator s∈S of (W,S) to be an intrinsic reflection of W.

AB - Let (W,S) be a Coxeter system and let s∈S. We call s a right-angled generator of (W,S) if st=ts or st has infinite order for each t∈S. We call s an intrinsic reflection of W if s∈RW for all Coxeter generating sets R of W. We give necessary and sufficient conditions for a right-angled generator s∈S of (W,S) to be an intrinsic reflection of W.

KW - Coxeter groups

KW - Isomorphism problem

KW - Reflections

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SP - 326

EP - 360

JO - Journal of Combinatorial Theory. Series A

JF - Journal of Combinatorial Theory. Series A

ER -

Intrinsic reflections in Coxeter systems

Abstract

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