A Frobenius formula for the structure coefficients of double-class algebras of Gelfand pairs

Abstract

We generalise some well known properties of irreducible characters of finite groups to zonal spherical functions of Gelfand pairs. This leads to 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 generalisation of the Frobenius formula which writes the structure coefficients of the center of a finite group algebra in terms of irreducible characters.

References in corpus (1)

• A general framework for the polynomiality property of the structure coefficients of double-class algebras

Cited by in corpus (4)

• A general framework for the polynomiality property of the structure coefficients of double-class algebras
• $k$-partial permutations and the center of the wreath product ${\mathcal{S}}_k\wr {\mathcal{S}}_n$ algebra
• Stability of the Hecke algebra of wreath products
• Stability of the centers of the symplectic groups rings $\matbb{Z}[Sp_{2n}(q)]$