Wreath product generalizations of the triple (S2n, Hn, φ) and their spherical functions

JOURNAL OF ALGEBRA

卷:334

Article

Mizukawa, Hiroshi

关键词: Finite spherical harmonics;    Gelfand triple;    Hecke algebra;    Zonal polynomial;    Schur function;    Schur's Q-function;   

DOI  :  10.1016/j.jalgebra.2011.02.036

来源: Elsevier

【 摘 要 】

The symmetric group S-2n and the hyperoctahedral group H-n is a Gelfand triple for an arbitrary linear representation phi of H-n. Their phi-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. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free