Non symmetric Cauchy kernels for the classical Groups

Amy M. Fu; Alain Lascoux

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arXiv · math/0612828

Non symmetric Cauchy kernels for the classical Groups

Amy M. Fu·Alain Lascoux

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Abstract

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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Amy M. Fu, Alain Lascoux. 2006-12-28. Non symmetric Cauchy kernels for the classical Groups. https://arxiv.org/abs/math/0612828

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