Non-symmetric Cauchy kernels for the classical groups |
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Authors: | Amy M Fu |
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Institution: | a Center for Combinatorics, LPMC, PCSIRT, Nankai University, 94 Weijin Road, Tianjin 300071, PR China b CNRS, IGM Université Paris-Est, Marne-la-Vallée, 77454 Marne-la-Vallée cedex, France |
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Abstract: | We give non-symmetric versions of the Cauchy kernel and Littlewood's kernels, corresponding to the types A, B, C and D, of the classical groups. Defining two families of key polynomials (one of them being the Demazure characters), we show that these new kernels are diagonal in the basis of key polynomials. We define scalar products such that the two families of key polynomials are adjoint to each other. |
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Keywords: | Cauchy kernel Littlewood's kernels Classical groups Key polynomials Isobaric divided differences |
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