Tableau Formulas for One-Row 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 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 {}_{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
- E-Print:
- SIGMA 11 (2015), 100, 21 pages