English

Tableau Formulas for One-Row Macdonald Polynomials of Types $C_n$ and $D_n$

Combinatorics 2015-12-08 v3

Abstract

We present explicit formulas for the Macdonald polynomials of types CnC_n and DnD_n in the one-row case. In view of the combinatorial structure, we call them "tableau formulas". For the construction of the tableau formulas, we apply some transformation formulas for the basic hypergeometric series involving very well-poised balanced 12W11{}_{12}W_{11} series. We remark that the correlation functions of the deformed W\mathcal{W} algebra generators automatically give rise to the tableau formulas when we principally specialize the coordinate variables.

Keywords

Cite

@article{arxiv.1412.8001,
  title  = {Tableau Formulas for One-Row Macdonald Polynomials of Types $C_n$ and $D_n$},
  author = {Boris Feigin and Ayumu Hoshino and Masatoshi Noumi and Jun Shibahara and Jun'ichi Shiraishi},
  journal= {arXiv preprint arXiv:1412.8001},
  year   = {2015}
}