Abstract
The symmetric group S 2 n and the hyperoctahedral group H n is a Gelfand triple for an arbitrary linear representation φ of H n . Their φ-spherical functions can be caught as a transition matrix between suitable symmetric functions and the power sums. We generalize this triplet in the term of wreath product. It is shown that our triplet is always a Gelfand triple. Furthermore we study the relation between their spherical functions and a multi-partition version of the ring of symmetric functions.
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