We compute the spherical functions on the symmetric space Sp 2n/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 Spn.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Macdonald polynomial
- Plancherel formula
- spherical function