Abstract Young representations for Coxeter groups of type D

Yona Cherniavsky

doi:10.1016/j.aam.2007.09.005

Abstract Young representations for Coxeter groups of type D

Yona Cherniavsky

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

Abstract

Abstract Young (briefly: AY) representations are Coxeter group representations which carry an extended Young form. These representations appear in a new axiomatic approach to the representation theory of Coxeter groups. While AY representations for Coxeter groups of types A and B are well understood, little is known about type D. We introduce D-Young tableaux and study minimal AY representations associated with them. The main result is a decomposition rule for the AY representations which are induced from S_n into D_n. The proof of this rule involves a combinatorial bijection together with theorems from complex analysis.

Original language	English
Pages (from-to)	561-583
Number of pages	23
Journal	Advances in Applied Mathematics
Volume	41
Issue number	4
DOIs	https://doi.org/10.1016/j.aam.2007.09.005
State	Published - Oct 2008
Externally published	Yes

Keywords

Abstract Young representations
Type-D Coxeter group
Young orthogonal form

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10.1016/j.aam.2007.09.005

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title = "Abstract Young representations for Coxeter groups of type D",

abstract = "Abstract Young (briefly: AY) representations are Coxeter group representations which carry an extended Young form. These representations appear in a new axiomatic approach to the representation theory of Coxeter groups. While AY representations for Coxeter groups of types A and B are well understood, little is known about type D. We introduce D-Young tableaux and study minimal AY representations associated with them. The main result is a decomposition rule for the AY representations which are induced from Sn into Dn. The proof of this rule involves a combinatorial bijection together with theorems from complex analysis.",

keywords = "Abstract Young representations, Type-D Coxeter group, Young orthogonal form",

author = "Yona Cherniavsky",

note = "Funding Information: ✩ Supported in part by a grant from the Israel Science Foundation, this work is a part of the author{\textquoteright}s PhD thesis, Department of Mathematics and Statistics, Bar-Ilan University, Ramat-Gan 52900, Israel. E-mail addresses: [email protected], [email protected].",

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AU - Cherniavsky, Yona

N1 - Funding Information: ✩ Supported in part by a grant from the Israel Science Foundation, this work is a part of the author’s PhD thesis, Department of Mathematics and Statistics, Bar-Ilan University, Ramat-Gan 52900, Israel. E-mail addresses: [email protected], [email protected].

PY - 2008/10

Y1 - 2008/10

N2 - Abstract Young (briefly: AY) representations are Coxeter group representations which carry an extended Young form. These representations appear in a new axiomatic approach to the representation theory of Coxeter groups. While AY representations for Coxeter groups of types A and B are well understood, little is known about type D. We introduce D-Young tableaux and study minimal AY representations associated with them. The main result is a decomposition rule for the AY representations which are induced from Sn into Dn. The proof of this rule involves a combinatorial bijection together with theorems from complex analysis.

AB - Abstract Young (briefly: AY) representations are Coxeter group representations which carry an extended Young form. These representations appear in a new axiomatic approach to the representation theory of Coxeter groups. While AY representations for Coxeter groups of types A and B are well understood, little is known about type D. We introduce D-Young tableaux and study minimal AY representations associated with them. The main result is a decomposition rule for the AY representations which are induced from Sn into Dn. The proof of this rule involves a combinatorial bijection together with theorems from complex analysis.

KW - Abstract Young representations

KW - Type-D Coxeter group

KW - Young orthogonal form

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SP - 561

EP - 583

JO - Advances in Applied Mathematics

JF - Advances in Applied Mathematics

IS - 4

ER -

Abstract Young representations for Coxeter groups of type D

Abstract

Keywords

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