Gelfand Triples and Their Hecke Algebras

Harmonic Analysis for Multiplicity-Free Induced Representations of Finite Groups

Tullio Ceccherini-Silberstein, Fabio Scarabotti, Filippo Tolli (Autoren)

Buch | Softcover

XVIII, 140 Seiten

2020 | 1st ed. 2020
Springer International Publishing (Verlag)
978-3-030-51606-2 (ISBN)

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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.

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 Theoretical Computer 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.

- 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.

"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)

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

Erscheinungsdatum	27.09.2020
Reihe/Serie	Lecture Notes in Mathematics
Vorwort	Eiichi Bannai
Zusatzinfo	XVIII, 140 p.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	253 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Schlagworte	Gelfand pair • General Linear Group over a Finite Field • Hecke algebra • induced representation • Spherical Function
ISBN-10	3-030-51606-7 / 3030516067
ISBN-13	978-3-030-51606-2 / 9783030516062
Zustand	Neuware