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Symmetric and non-symmetric quantum Capelli polynomials

Friedrich Knop
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Abstract

We define a family of symmetric and a family of non-symmetric polynomials in terms of vanishing conditions. These families depend on two paramters, q and t. Their main feature is that they consist of non-homogeneous polynomials. The symmetric polynomials form the quantized version of polynomials occuring in the context of generalized Capelli identities. We show that these quantum Capelli polynomials are also characterized by q-difference equations. More precisely, they are eigenfunctions of Cherednik type operators and transform under an affine Hecke algebra. Thus, we are able to identify their top homogeneous component as a Macdonald polynomial (symmetric or non-symmetric, respectively).

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Friedrich Knop. 1996-03-29. Symmetric and non-symmetric quantum Capelli polynomials. https://doi.org/10.4171/cmh%2F72.1.7

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