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arxiv: q-alg/9610014 · v1 · submitted 1996-10-11 · q-alg · math.QA

A reproducing kernel for nonsymmetric Macdonald polynomials

K. Mimachi , M. Noumi This is my paper
classification q-alg math.QA
keywords formulakernelmacdonaldnonsymmetricpolynomialsreproducingcauchyeigenfunctions
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We present a new formula of Cauchy type for the nonsymmetric Macdonald polynomials which are joint eigenfunctions of q-Dunkl operators. This gives the explicit formula for a reproducing kernel on the polynomial ring of n variables.

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  1. Symmetric polynomials: DIM integrable systems versus twisted Cherednik systems

    hep-th 2026-01 unverdicted novelty 7.0

    For t = q^{-m}, eigenfunctions from DIM Hamiltonians and twisted Cherednik Hamiltonians combine into identical symmetric functions that are eigenfunctions of both systems simultaneously.