Hecke algebras and harmonic analysis on finite groups

Let G be a finite group, K a subgroup and (σ, V ) an irreducible representation of K. Then the Hecke algebra associated with the triple (G, K, σ) is the commutant of the induced representation Ind^G_K σ. In [3] Curtis and Fossum derived several explicit expressions for the characters of Hecke algebr...

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Main Authors:	Fabio Scarabotti, Filippo Tolli
Format:	Article
Language:	English
Published:	Sapienza Università Editrice 2013-01-01
Series:	Rendiconti di Matematica e delle Sue Applicazioni
Subjects:	hecke algebra irreducible character spherical function
Online Access:	https://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/2013(1-2)/27-52.pdf

id	doaj-ecacf1b70a94490ba8d0dee9ba52ef67
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spelling	doaj-ecacf1b70a94490ba8d0dee9ba52ef672021-04-27T20:06:50ZengSapienza Università EditriceRendiconti di Matematica e delle Sue Applicazioni1120-71832532-33502013-01-01331-22752Hecke algebras and harmonic analysis on finite groupsFabio Scarabotti0Filippo Tolli1Sapienza Università di RomaUniversità Roma TRELet G be a finite group, K a subgroup and (σ, V ) an irreducible representation of K. Then the Hecke algebra associated with the triple (G, K, σ) is the commutant of the induced representation Ind^G_K σ. In [3] Curtis and Fossum derived several explicit expressions for the characters of Hecke algebras. In the present paper we give an exposition of their results (see also [5], pp. 279-291) in the language of finite harmonic analysis. In particular, we show the connection with the theory of finite Gelfand pairs. https://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/2013(1-2)/27-52.pdfhecke algebrairreducible characterspherical function
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Fabio Scarabotti Filippo Tolli
spellingShingle	Fabio Scarabotti Filippo Tolli Hecke algebras and harmonic analysis on finite groups Rendiconti di Matematica e delle Sue Applicazioni hecke algebra irreducible character spherical function
author_facet	Fabio Scarabotti Filippo Tolli
author_sort	Fabio Scarabotti
title	Hecke algebras and harmonic analysis on finite groups
title_short	Hecke algebras and harmonic analysis on finite groups
title_full	Hecke algebras and harmonic analysis on finite groups
title_fullStr	Hecke algebras and harmonic analysis on finite groups
title_full_unstemmed	Hecke algebras and harmonic analysis on finite groups
title_sort	hecke algebras and harmonic analysis on finite groups
publisher	Sapienza Università Editrice
series	Rendiconti di Matematica e delle Sue Applicazioni
issn	1120-7183 2532-3350
publishDate	2013-01-01
description	Let G be a finite group, K a subgroup and (σ, V ) an irreducible representation of K. Then the Hecke algebra associated with the triple (G, K, σ) is the commutant of the induced representation Ind^G_K σ. In [3] Curtis and Fossum derived several explicit expressions for the characters of Hecke algebras. In the present paper we give an exposition of their results (see also [5], pp. 279-291) in the language of finite harmonic analysis. In particular, we show the connection with the theory of finite Gelfand pairs.
topic	hecke algebra irreducible character spherical function
url	https://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/2013(1-2)/27-52.pdf
work_keys_str_mv	AT fabioscarabotti heckealgebrasandharmonicanalysisonfinitegroups AT filippotolli heckealgebrasandharmonicanalysisonfinitegroups
_version_	1721505720966316032

Hecke algebras and harmonic analysis on finite groups

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