Gelfand Triples and Their Hecke Algebras

Harmonic Analysis for Multiplicity-Free Induced Representations of Finite Groups
1. Auflage 2020
ISBN: 978-3-030-51606-2
Verlag: Springer International Publishing

Buch, Englisch, Band 2267, 140 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 254 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Ceccherini-Silberstein, Tullio

Scarabotti, Fabio

Tolli, Filippo

Weitere Mitwirkende

Bannai, Eiichi

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie
• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionentheorie, Komplexe Analysis

Inhaltsverzeichnis

Foreword.- Preface.- 1 Preliminaries.- 2 Hecke algebras.- 3 Multiplicity-free triples.- 4 The case of a normal subgroup.- 5 Harmonic Analysis of the multiplicity-free triple (GL(2, Fq),C,n ).- 6 Harmonic analysis of the multiplicity-free triple.- A Appendix.- Index.

Über Autor(innen)

Tullio Ceccherini-Silberstein obtained his BS in Mathematics (1990) from the University of Rome “La Sapienza” and his PhD in Mathematics (1994) from UCLA. Currently, he is professor of Mathematical Analysis at the University of Sannio (Benevento). He is an Editor of the EMS journal “Groups, Geometry, and Dynamics”. He has authored more than 90 research articles in Functional and Harmonic Analysis, Group Theory, Ergodic Theory and Dynamical Systems, and Theoretical Computer Science and has co-authored 5 monographs on Harmonic Analysis and Representation Theory. 
Fabio Scarabotti obtained his BS in Mathematics (1989) and his PhD in Mathematics (1994) from the University of Rome “La Sapienza”.  Currently, he is professor of Mathematical Analysis at the University of Rome “La Sapienza”. He has authored more than 40 research articles in Harmonic Analysis, Group Theory, Combinatorics, Ergodic Theory and Dynamical Systems, and TheoreticalComputer Science and has co-authored 4 monographs on Harmonic Analysis and Representation Theory.
Filippo Tolli obtained his BS in Mathematics (1991) from the University of Rome “La Sapienza” and his PhD in Mathematics (1996) from UCLA. Currently, he is professor of Mathematical Analysis at the University of Roma Tre. He has authored more than 30 research articles in Harmonic Analysis, Group Theory, Combinatorics, Lie Groups and Partial Differential Equations and has co-authored 4 monographs on Harmonic Analysis and Representation Theory.