Combinatorial formula for Macdonald polynomials, Bethe Ansatz, and generic Macdonald polynomials

Details Combinatorial formula for Macdonald polynomials, Bethe Ansatz, and generic Macdonald polynomials Combinatorial formula for Macdonald polynomials, Bethe Ansatz, and generic Macdonald polynomials

2000-08-13

arxiv.org/abs/math/0008094v1

Mathematics

Quantum Algebra

Latex, 18 pages, no figures

Scientific paper

We give a direct proof of the combinatorial formula for interpolation Macdonald polynomials by introducing certain polynomials, which we call generic Macdonald polynomials, which depend on $d$ additional parameters and specialize to all Macdonald polynomials of degree $d$. The form of these generic polynomials is that of a Bethe eigenfunction and they imitate, on a more elementary level, the $R$-matrix construction of quantum immanants.

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