Non-symmetric Cauchy kernels for the classical groups

作者：Fu Amy M^*; Lascoux Alain

来源：Journal of Combinatorial Theory - Series A, 2009, 116(4): 903-917.

DOI：10.1016/j.jcta.2008.10.007

• Cauchy kernel
• Littlewood's kernels
• Classical groups
• Key polynomials
• Isobaric divided differences

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.

• 出版日期2009-5
• 单位南开大学