A raising operator formula for Macdonald polynomialsAlgebra & Discrete Mathematics
|Anna Pun, CUNY-Baruch College
|Thu, Feb 16 2023, 1:10PM
In this talk, I will give a brief introduction on Catalanimal, a tool that helps us to prove the shuffle theorem under any line, the extended delta conjecture and the Loehr-Warrington conjecture. I will then focus on its variant "Macanimal" which gives us an explicit raising operator formula for the modified Macdonald polynomials. Our method just as easily yields a formula for an infinite series of $GL_l$ characters which truncates to the modified Macdonald polynomials.
This is a joint work with Jonah Blasiak, Mark Haiman, Jennifer Morse and George Seelinger.