Tableau Formulas for OneRow Macdonald Polynomials of Types C_n and D_n
Abstract
We present explicit formulas for the Macdonald polynomials of types C_n and D_n in the onerow 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 wellpoised balanced {}_{12}W_{11} series. We remark that the correlation functions of the deformed W algebra generators automatically give rise to the tableau formulas when we principally specialize the coordinate variables.
 Publication:

SIGMA
 Pub Date:
 December 2015
 DOI:
 10.3842/SIGMA.2015.100
 arXiv:
 arXiv:1412.8001
 Bibcode:
 2015SIGMA..11..100F
 Keywords:

 Macdonald polynomials;
 deformed W algebras;
 Mathematics  Combinatorics
 EPrint:
 SIGMA 11 (2015), 100, 21 pages