Non symmetric Cauchy kernels for the classical Groups

Details Non symmetric Cauchy kernels for the classical Groups Non symmetric Cauchy kernels for the classical Groups

2006-12-28

arxiv.org/abs/math/0612828v1

Mathematics

Combinatorics

Scientific paper

We give non-symmetric versions of the Cauchy kernel and Littlewood's kernels, corresponding to the types $A_n$, $B_n$, $C_n$ and $D_n$, of the classical groups. We show that these new kernels are diagonal in the basis of two families of key polynomials (one of them being Demazure characters) obtained as images of dominant monomials under isobaric divided differences. We define scalar products such that the two families of key polynomials are adjoint to each other.

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