Hiroshi Mizukawa

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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(More)
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(More)
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