37 research outputs found
Wreath Product Generalizations of the Triple and Their Spherical Functions
The symmetric group and the hyperoctaheadral group is a
Gelfand triple for an arbitrary linear representation of . Their
-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.Comment: 25 page
Orthogonality Relations for Multivariate Krawtchouk Polynomials
The orthogonality relations of multivariate Krawtchouk polynomials are
discussed. In case of two variables, the necessary and sufficient conditions of
orthogonality is given by Gr\"unbaum and Rahman in [SIGMA 6 (2010), 090, 12
pages, arXiv:1007.4327]. In this study, a simple proof of the necessary and
sufficient condition of orthogonality is given for a general case
Orthogonal polynomials arising from the wreath products of a dihedral group with a symmetric group
AbstractSome classes of orthogonal polynomials are discussed in this paper which are expressed in terms of (n+1,m+1)-hypergeometric functions. The orthogonality comes from that of zonal spherical functions of certain Gelfand pairs
Mixed expansion formula for the rectangular Schur functions and the affine Lie algebra A_1^(1)
Formulas are obtained that express the Schur S-functions indexed by Young
diagrams of rectangular shape as linear combinations of "mixed" products of
Schur's S- and Q-functions. The proof is achieved by using representations of
the affine Lie algebra of type A_1^{(1)}. A realization of the basic
representation that is of ``D_2^{(2)}''-type plays the central role.Comment: 21page