Wreath Product Generalizations of the Triple (S_2n,H_n,ϕ) and Their Spherical Functions

2009/08/21 by Hiroshi Mizukawa, Mizukawa, Hiroshi
Chemistry · Mathematics · #05E05 #05E10 #05E35 #20C05 #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Molecular spectroscopy and chirality #Representation Theory (math.RT) #math.CO #math.RT #msc:05E05 #msc:05E10 #msc:05E35 #msc:20C05

paper · pdf · doi:10.48550/arxiv.0908.3056

25 pages

openalex publication_date 2009/08/21 · arxiv created 2010/10/12 · arxiv updated 2010/10/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

The symmetric group S_2n and the hyperoctaheadral group H_n is a Gelfand triple for an arbitrary linear representation ϕ of H_n. Their ϕ-spherical functions can be caught as 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 are always to be a Gelfand triple. Furthermore we study the relation between their spherical functions and multi-partition version of the ring of symmetric functions.

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