Hecke algebras and harmonic analysis on finite groups

Abstract

Let G be a finite group, K a subgroup and (σ, V ) an irreducible representation of K. Then the Hecke algebra associated with the triple (G, K, σ) is the commutant of the induced representation Ind^G_K σ. In [3] Curtis and Fossum derived several explicit expressions for the characters of Hecke algebras. In the present paper we give an exposition of their results (see also [5], pp. 279-291) in the language of finite harmonic analysis. In particular, we show the connection with the theory of finite Gelfand pairs.

Keywords

• hecke algebra
• irreducible character
• spherical function