Tullio Ceccherini-Silberstein, Fabio Scarabotti, Filippo Tolli

Gelfand Triples and Their Hecke Algebras

Harmonic Analysis for Multiplicity-Free Induced Representations of Finite Groups
Mitarbeit:Bannai, Eiichi

• Broschiertes Buch

Produktbeschreibung

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.

Produktdetails

• Lecture Notes in Mathematics 2267
• Verlag: Springer / Springer International Publishing / Springer, Berlin
• Artikelnr. des Verlages: 978-3-030-51606-2
• 1st ed. 2020
• Seitenzahl: 160
• Erscheinungstermin: 26. September 2020
• Englisch
• Abmessung: 235mm x 155mm x 9mm
• Gewicht: 254g
• ISBN-13: 9783030516062
• ISBN-10: 3030516067
• Artikelnr.: 59493671

Autorenporträt

Tullio Ceccherini-Silberstein graduated from the University of Rome La Sapienza in 1990 and obtained his PhD in mathematics at the University of California at Los Angeles in 1994. Since 1997 he has been professor of Mathematical Analysis at the University of Sannio, Benevento (Italy). His main interests include harmonic and functional analysis, geometric and combinatorial group theory, ergodic theory and dynamical systems, and theoretical computer science. He is an editor of the journal Groups, Geometry, and Dynamics, published by the European Mathematical Society, and of the Bulletin of the Iranian Mathematical Society. He has published more than 90 research papers, 9 monographs, and 4 conference proceedings. Professor Michel Coornaert taught mathematics at the University of Strasbourg from 1992 until 2021. His research interests are in geometry, topology, group theory and dynamical systems. He is the author of many Springer volumes,including Topological Dimension and Dynamical Systems (2015), Cellular Automata and Groups (2010), Symbolic Dynamics and Hyperbolic Groups (1993) and Géométrie et théorie des groupes (1990).

Inhaltsangabe

- Preliminaries. - Hecke Algebras. - Multiplicity-Free Triples. - The Case of a Normal Subgroup. - Harmonic Analysis of the Multiplicity-Free Triple (GL(2, Fq),C, ni). - Harmonic Analysis of the Multiplicity-Free Triple (GL(2, Fq2),GL(2, Fq), ni). - Appendix A.

Rezensionen

"The volume is an interesting and important contribution to the theory of multiplicity-free representations of finite groups and their spherical functions." (Antoni Wawrzynczyk, Mathematical Reviews, June, 2023)