2015-07-03(q, t)-hook formula for d-complete posets
Masao Ishikawa (University of the Ryukyus)
Okada showed that a (q,t)-analogue of the hook formula holds for the Young diagrams and the shifted diagrams, and made a general conjecture for d-complete posets. Proctor defined the d-complete posets combinatorially and classified them into 15 irreducible ones which includes the Shapes (Young diagrams) and the Shifted Shapes (shifted Young diagrams). We give a proof of his conjecture for Birds and Banners using the Pierri rules of the Macdonald polynomials and Gasper’s identity for very well poised series 12W11.