03241nam 22007455 450 991048359960332120251113202753.03-030-51607-510.1007/978-3-030-51607-9(OCoLC)1201562589(CKB)4100000011469524(MiAaPQ)EBC6357670(DE-He213)978-3-030-51607-9(PPN)250220474(MiAaPQ)EBC6357660(EXLCZ)99410000001146952420200925d2020 u| 0engurnn#008mamaatxtrdacontentcrdamediacrrdacarrierGelfand Triples and Their Hecke Algebras Harmonic Analysis for Multiplicity-Free Induced Representations of Finite Groups /by Tullio Ceccherini-Silberstein, Fabio Scarabotti, Filippo Tolli1st ed. 2020.Cham :Springer International Publishing :Imprint: Springer,2020.1 online resource (XVIII, 140 p.)Lecture Notes in Mathematics,1617-9692 ;22673-030-51606-7 This monograph is the first comprehensive treatment of multiplicity-free induced representations of finite groups as a generalization of finite Gelfand pairs. Up to now, researchers have been somehow reluctant to face such a problem in a general situation, and only partial results were obtained in the one-dimensional case. Here, for the first time, new interesting and important results are proved. In particular, after developing a general theory (including the study of the associated Hecke algebras and the harmonic analysis of the corresponding spherical functions), two completely new highly nontrivial and significant examples (in the setting of linear groups over finite fields) are examined in full detail. The readership ranges from graduate students to experienced researchers in Representation Theory and Harmonic Analysis.Lecture Notes in Mathematics,1617-9692 ;2267Harmonic analysisGroup theoryFourier analysisAssociative ringsAssociative algebrasSpecial functionsAbstract Harmonic AnalysisGroup Theory and GeneralizationsFourier AnalysisAssociative Rings and AlgebrasSpecial FunctionsHarmonic analysis.Group theory.Fourier analysis.Associative rings.Associative algebras.Special functions.Abstract Harmonic Analysis.Group Theory and Generalizations.Fourier Analysis.Associative Rings and Algebras.Special Functions.515.2433515.785Ceccherini-Silberstein Tullio503338Scarabotti FabioTolli Filippo1968-Bannai EiichiMiAaPQMiAaPQMiAaPQBOOK9910483599603321Gelfand triples and their Hecke algebras2278687UNINA