Hecke algebras and harmonic analysis on finite groups

Let G be a finite group, K a subgroup and V an irreducible representation of K. Then the Hecke algebra associated with the triple (G,K,V ) is the commutant of hte representation obtained inducing V from K to G. Curtis and Fossum derived several explicit expressions for the characters of Hecke algebras. In the present paper we give an exposition of their results in the language of finite harmonic analysis. In particular, we show the connection with the theory of finite Gelfand pairs.