Spherical functions on as a spherical homogeneous -space

✍ Scribed by Yumiko Hironaka

• Book ID: 104024509
• Publisher: Elsevier Science
• Year: 2005
• Tongue: English
• Weight: 460 KB
• Volume: 112
• Category: Article
• ISSN: 0022-314X
• DOI: 10.1016/j.jnt.2004.08.012

✦ Synopsis

We investigate spherical functions on Sp 2 as a spherical homogeneous G=Sp 2 ×(Sp 1 ) 2 -space over a p-adic field k, which form a 4-dimensional vector space for each eigenvalue given by Satake parameter. Explicit expressions of spherical functions and Cartan decomposition of Sp 2 are given. Using spherical transform, we determine Hecke module structure of the Schwartz-Bruhat space S(K\Sp 2 ), which is free of rank 4.