Combinatorial Formulas for Macdonald and Hall-Littlewood Polynomials
Abstrak
A breakthrough in the theory of (type $A$) Macdonald polynomials is due to Haglund, Haiman and Loehr, who exhibited a combinatorial formula for these polynomials in terms of fillings of Young diagrams. Recently, Ram and Yip gave a formula for the Macdonald polynomials of arbitrary type in terms of the corresponding affine Weyl group. In this paper, we show that a Haglund-Haiman-Loehr type formula follows naturally from the more general Ram-Yip formula, via compression. Then we extend this approach to the Hall-Littlewood polynomials of type $C$, which are specializations of the corresponding Macdonald polynomials at $q=0$. We note that no analog of the Haglund-Haiman-Loehr formula exists beyond type $A$, so our work is a first step towards finding such a formula.
Topik & Kata Kunci
Penulis (1)
Cristian Lenart
Akses Cepat
- Tahun Terbit
- 2009
- Sumber Database
- DOAJ
- DOI
- 10.46298/dmtcs.2695
- Akses
- Open Access ✓