Skip Navigation



Proceedings of the London Mathematical Society Advance Access published online on August 17, 2009
Proceedings of the London Mathematical Society, doi:10.1112/plms/pdp027
This Article
Right arrow FREE Full Text (PDF) Freely available
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Scarabotti, F.
Right arrow Articles by Tolli, F.
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© 2009 London Mathematical Society

Harmonic analysis on a finite homogeneous space

Fabio Scarabotti

Dipartimento MeMoMat
Università degli Studi di Roma "La Sapienza"
via A. Scarpa 8
00161 Roma
Italy

Filippo Tolli

Dipartimento di Matematica
Università Roma TRE
L. San Leonardo Murialdo 1
00146 Roma
Italy
tolli@mat.uniroma3.it

Received 26 January 2007. Revision received 9 June 2008. Accepted 9 June 2008.

In this paper, we study harmonic analysis on finite homogeneous spaces whose associated permutation representation decomposes with multiplicity. After a careful look at Frobenius reciprocity and transitivity of induction, we introduce three types of spherical functions. Then we consider the composition of two permutation representations, giving a noncommutative generalization of the Gelfand pair associated to the ultrametric space; actually, we study the more general notion of crested product. Finally, we consider the exponentiation action, generalizing the decomposition of the Gelfand pair of the Hamming scheme; actually, we study a more general construction that we call wreath product of permutation representations, suggested by the study of finite lamplighter random walks. We give several examples of concrete decompositions of permutation representations and several explicit ‘rules’ of decomposition.

2000 Mathematics Subject Classification 43A95 (primary), 20C15, 20C30, 20E22, 43A90 (secondary).


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer: Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.