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A raising operator formula for Macdonald polynomials

Algebra & Discrete Mathematics

Speaker: Anna Pun, CUNY-Baruch College
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Location: zoom zoom
Start time: 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.