Strong Reality Properties of Normalizers of Parabolic Subgroups in Finite Coxeter Groups

Klaus Lux; Amanda Schaeffer Fry; C. Ryan Vinroot

doi:10.1080/00927872.2011.563372

Strong Reality Properties of Normalizers of Parabolic Subgroups in Finite Coxeter Groups

Klaus Lux, Amanda Schaeffer Fry, C. Ryan Vinroot

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

3 Scopus citations

Abstract

Let W be a finite Coxeter group, P a parabolic subgroup of W, and N _W(P) the normalizer of P in W. We prove that every element in N _W(P) is strongly real in N _W(P), and that every irreducible complex character of N _W(P) has Frobenius-Schur indicator 1.

Original language	English (US)
Pages (from-to)	3056-3070
Number of pages	15
Journal	Communications in Algebra
Volume	40
Issue number	8
DOIs	https://doi.org/10.1080/00927872.2011.563372
State	Published - Aug 2012
Externally published	Yes

Keywords

Finite Coxeter group
Frobenius-Schur indicator
Normalizers of parabolic subgroups
Strong reality

ASJC Scopus subject areas

Algebra and Number Theory

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10.1080/00927872.2011.563372

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title = "Strong Reality Properties of Normalizers of Parabolic Subgroups in Finite Coxeter Groups",

abstract = "Let W be a finite Coxeter group, P a parabolic subgroup of W, and N W(P) the normalizer of P in W. We prove that every element in N W(P) is strongly real in N W(P), and that every irreducible complex character of N W(P) has Frobenius-Schur indicator 1.",

keywords = "Finite Coxeter group, Frobenius-Schur indicator, Normalizers of parabolic subgroups, Strong reality",

author = "Klaus Lux and Fry, {Amanda Schaeffer} and Vinroot, {C. Ryan}",

note = "Funding Information: The authors thank the referee for carefully reading this article. The second author was supported in part by a graduate fellowship from the National Physical Science Consortium, and the third author was supported in part by NSF grant DMS-0854849.",

year = "2012",

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doi = "10.1080/00927872.2011.563372",

language = "English (US)",

volume = "40",

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journal = "Communications in Algebra",

issn = "0092-7872",

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TY - JOUR

T1 - Strong Reality Properties of Normalizers of Parabolic Subgroups in Finite Coxeter Groups

AU - Lux, Klaus

AU - Fry, Amanda Schaeffer

AU - Vinroot, C. Ryan

N1 - Funding Information: The authors thank the referee for carefully reading this article. The second author was supported in part by a graduate fellowship from the National Physical Science Consortium, and the third author was supported in part by NSF grant DMS-0854849.

PY - 2012/8

Y1 - 2012/8

N2 - Let W be a finite Coxeter group, P a parabolic subgroup of W, and N W(P) the normalizer of P in W. We prove that every element in N W(P) is strongly real in N W(P), and that every irreducible complex character of N W(P) has Frobenius-Schur indicator 1.

AB - Let W be a finite Coxeter group, P a parabolic subgroup of W, and N W(P) the normalizer of P in W. We prove that every element in N W(P) is strongly real in N W(P), and that every irreducible complex character of N W(P) has Frobenius-Schur indicator 1.

KW - Finite Coxeter group

KW - Frobenius-Schur indicator

KW - Normalizers of parabolic subgroups

KW - Strong reality

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DO - 10.1080/00927872.2011.563372

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VL - 40

SP - 3056

EP - 3070

JO - Communications in Algebra

JF - Communications in Algebra

IS - 8

ER -

Strong Reality Properties of Normalizers of Parabolic Subgroups in Finite Coxeter Groups

Abstract

Keywords

ASJC Scopus subject areas

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