English

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

Quantum Algebra 2007-05-23 v1 Combinatorics Representation Theory

Abstract

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 dd additional parameters and specialize to all Macdonald polynomials of degree dd. The form of these generic polynomials is that of a Bethe eigenfunction and they imitate, on a more elementary level, the RR-matrix construction of quantum immanants.

Keywords

Cite

@article{arxiv.math/0008094,
  title  = {Combinatorial formula for Macdonald polynomials, Bethe Ansatz, and generic Macdonald polynomials},
  author = {Andrei Okounkov},
  journal= {arXiv preprint arXiv:math/0008094},
  year   = {2007}
}

Comments

Latex, 18 pages, no figures