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FIELD
Math: HCMC
DATE
Apr 12 (Fri), 2024
TIME
10:00 ~ 11:00
PLACE
ONLINE
SPEAKER
Wen, Joshua
HOST
Oh, Jaeseong
INSTITUTE
Northeastern University
TITLE
Wreath Macdonald polynomials
ABSTRACT
Defined by Haiman, wreath Macdonald polynomials are generalizations of the well-known Macdonald polynomials to wreath products of cyclic groups with symmetric groups. For a fixed cylic group Z/rZ, these can be viewed as partially-symmetric polynomials, where there are r families of symmetric variables. Many results for the usual Macdonald polynomials should have analogues in the wreath setting: e.g. Macdonald operators, bispectral duality, evaluation formulas, and norm formulas. Precise conjectures for these analogues can be tricky to write down and even more difficult to prove. A guiding principle is that various quantum algebraic methods in the classical Macdonald theory should have generalizations in the wreath setting. I will present work, joint with Daniel Orr and Mark Shimozono, that studies these polynomials via the rank r quantum toroidal algebra.
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