Symmetric and non-symmetric quantum Capelli polynomials

Details Symmetric and non-symmetric quantum Capelli polynomials Symmetric and non-symmetric quantum Capelli polynomials

1996-03-29

arxiv.org/abs/q-alg/9603028v1

Comment. Math. Helv. 72 (1997), 84-100

Mathematics

Quantum Algebra

15 pages

Scientific paper

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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