On the invariants of the cohomology of complements of Coxeter arrangements

J. Matthew Douglass; Götz Pfeiffer; Gerhard Röhrle

doi:10.1016/j.jalgebra.2019.05.010

On the invariants of the cohomology of complements of Coxeter arrangements

J. Matthew Douglass, Götz Pfeiffer, Gerhard Röhrle

Mathematics

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Abstract

We refine Brieskorn's study of the cohomology of the complement of the reflection arrangement of a finite Coxeter group W. As a result we complete the verification of a conjecture by Felder and Veselov that gives an explicit basis of the space of W-invariants in this cohomology ring.

Original language	English
Pages (from-to)	336-349
Number of pages	14
Journal	Journal of Algebra
Volume	558
DOIs	https://doi.org/10.1016/j.jalgebra.2019.05.010
Publication status	Published - 15 Sep 2020

Keywords

Arrangements of hyperplanes
Coxeter groups
Hyperplane complements
Orlik-Solomon algebras

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10.1016/j.jalgebra.2019.05.010

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title = "On the invariants of the cohomology of complements of Coxeter arrangements",

abstract = "We refine Brieskorn's study of the cohomology of the complement of the reflection arrangement of a finite Coxeter group W. As a result we complete the verification of a conjecture by Felder and Veselov that gives an explicit basis of the space of W-invariants in this cohomology ring.",

keywords = "Arrangements of hyperplanes, Coxeter groups, Hyperplane complements, Orlik-Solomon algebras",

author = "Douglass, \{J. Matthew\} and G{\"o}tz Pfeiffer and Gerhard R{\"o}hrle",

note = "Publisher Copyright: {\textcopyright} 2019 Elsevier Inc.",

year = "2020",

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doi = "10.1016/j.jalgebra.2019.05.010",

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T1 - On the invariants of the cohomology of complements of Coxeter arrangements

AU - Douglass, J. Matthew

AU - Pfeiffer, Götz

AU - Röhrle, Gerhard

PY - 2020/9/15

Y1 - 2020/9/15

N2 - We refine Brieskorn's study of the cohomology of the complement of the reflection arrangement of a finite Coxeter group W. As a result we complete the verification of a conjecture by Felder and Veselov that gives an explicit basis of the space of W-invariants in this cohomology ring.

AB - We refine Brieskorn's study of the cohomology of the complement of the reflection arrangement of a finite Coxeter group W. As a result we complete the verification of a conjecture by Felder and Veselov that gives an explicit basis of the space of W-invariants in this cohomology ring.

KW - Arrangements of hyperplanes

KW - Coxeter groups

KW - Hyperplane complements

KW - Orlik-Solomon algebras

UR - http://www.scopus.com/inward/record.url?scp=85085631147&partnerID=8YFLogxK

U2 - 10.1016/j.jalgebra.2019.05.010

DO - 10.1016/j.jalgebra.2019.05.010

M3 - Article

SN - 0021-8693

VL - 558

SP - 336

EP - 349

JO - Journal of Algebra

JF - Journal of Algebra

ER -

On the invariants of the cohomology of complements of Coxeter arrangements

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Keywords

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