After a careful consideration of some of the well known properties of irreducible characters of finite groups to zonal spherical functions of Gelfand pairs, we were able to deduce a Frobenius formula for Gelfand pairs. For a given Gelfand pair, the structure coeﬃcients of its associated double-class algebra can be written in terms of zonal spherical functions. This is a generalization of the Frobenius formula which expresses the structure coeﬃcients of the center of a finite group algebra in terms of irreducible characters.
- Double-class algebras
- Gelfand pairs and zonal spherical functions
- group algebras
- representation theory of finite groups
- structure coeﬃcients
ASJC Scopus subject areas
- Algebra and Number Theory