Non symmetric Cauchy kernels for the classical Groups
组合数学
2007-05-23 v1
摘要
We give non-symmetric versions of the Cauchy kernel and Littlewood's kernels, corresponding to the types , , and , 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.
引用
@article{arxiv.math/0612828,
title = {Non symmetric Cauchy kernels for the classical Groups},
author = {Amy M. Fu and Alain Lascoux},
journal= {arXiv preprint arXiv:math/0612828},
year = {2007}
}