Lecture Notes in Mathematics

Gelfand Triples and Their Hecke Algebras

Harmonic Analysis for Multiplicity-Free Induced Representations of Finite Groups

Authors: Ceccherini-Silberstein, Tullio, Scarabotti, Fabio, Tolli, Filippo

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  • This is the first book on an essentially new subject. It will serve as a reference for future developments.
  • The treatment is self-contained and therefore accessible to a wide audience.
  • All arguments are presented in full generality.
  • Includes two new highly nontrivial and significant examples which are analyzed in full detail.
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About this book

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.

About the authors

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.

Table of contents (6 chapters)

Table of contents (6 chapters)

Buy this book

eBook 37,44 €
price for Spain (gross)
  • ISBN 978-3-030-51607-9
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 46,79 €
price for Spain (gross)
  • ISBN 978-3-030-51606-2
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Gelfand Triples and Their Hecke Algebras
Book Subtitle
Harmonic Analysis for Multiplicity-Free Induced Representations of Finite Groups
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
2267
Copyright
2020
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-51607-9
DOI
10.1007/978-3-030-51607-9
Softcover ISBN
978-3-030-51606-2
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XVIII, 140
Topics