A reproducing kernel for nonsymmetric Macdonald polynomials
classification
q-alg
math.QA
keywords
formulakernelmacdonaldnonsymmetricpolynomialsreproducingcauchyeigenfunctions
read the original abstract
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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Forward citations
Cited by 2 Pith papers
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Symmetric polynomials: DIM integrable systems versus twisted Cherednik systems
For t = q^{-m}, eigenfunctions from DIM Hamiltonians and twisted Cherednik Hamiltonians combine into identical symmetric functions that are eigenfunctions of both systems simultaneously.
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Twisted Cherednik spectrum as a $q,t$-deformation
The twisted Cherednik spectrum is a q,t-deformation of the polynomial eigenfunctions built from symmetric ground states and weak-composition excitations at q=1.
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