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A Plancherel formula for Sp2n/Spn×Spn and its application

Part of: Abstract harmonic analysis Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  01 March 2009

Zhengyu Mao  and
Stephen Rallis
Zhengyu Mao
Affiliation:
Department of Mathematics and Computer Science, Rutgers University, Newark, NJ 07102-1811, USA (email: zmao@rutgers.edu)
Stephen Rallis
Affiliation:
Department of Mathematics, The Ohio State University, Columbus, OH 43210, USA (email: haar@math.ohio-state.edu)
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Abstract

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We compute the spherical functions on the symmetric space Sp2n/Spn×Spn and derive a Plancherel formula for functions on the symmetric space. As an application of the Plancherel formula, we prove an identity which amounts to the fundamental lemma of a relative trace identity between Sp2n and $\widetilde {{\rm Sp}}_n$.

Keywords

spherical functionMacdonald polynomialPlancherel formula

MSC classification

Secondary: 43A90: Spherical functions 11F72: Spectral theory; Selberg trace formula

Information

Type
Research Article
Information
Compositio Mathematica , Volume 145 , Issue 2 , March 2009 , pp. 501 - 527
Copyright
Copyright © Foundation Compositio Mathematica 2009

References

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