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Journals and Conferences
The pair of groups, symmetric group S2n and hyperoctohedral group Hn , form a Gelfand pair. The characteristic map is a mapping from the graded algebra generated by the zonal spherical functions of (S2n, Hn) into the ring of symmetric functions. The images of the zonal spherical functions under this map are called the zonal polynomials. A wreath product… (More)
An expression is given for the plethysm p2 ◦ S , where p2 is the power sum of degree two and S is the Schur function indexed by a rectangular partition. The formula can be well understood from the viewpoint of the basic representation of the affine Lie algebra of type A (2) 2
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 Sand 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.
The orthogonality relations of multivariate Krawtchouk polynomials are discussed. In case of two variables, the necessary and sufficient conditions of orthogonality is given by Grünbaum and Rahman in [SIGMA 6 (2010), 090, 12 pages]. In this study, a simple proof of the necessary and sufficient condition of orthogonality is given for a general case.
A new basis for the polynomial ring of infinitely many variables is constructed which consists of products of Schur functions and Q-functions. The transition matrix from the natural Schur function basis is investigated.
The symmetric group S2n and the hyperoctaheadral group Hn is a Gelfand triple for an arbitrary linear representation φ of Hn. 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… (More)
The aim of this note is to introduce a compound basis for the space of symmetric functions. Our basis consists of products of Schur functions and Q-functions. The basis elements are indexed by the partitions. It is well known that the Schur functions form an orthonormal basis for our space. A natural question arises. How are these two bases connected? In… (More)