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Combinatorics Seminar

A raising operator formula for nabla on an LLT polynomial
Friday, February 4, 2022
3:00-4:00 PM
4088 East Hall Map
The operator nabla plays an important role in the theory of Macdonald polynomials and (q,t)-combinatorics. Over the past few decades, many combinatorial formulas for the image of various symmetric function bases under the nabla operator have been conjectured and eventually proven. The operator nabla also appeared in the study of the elliptic Hall algebra of Burban and Schiffmann, which is generated by subalgebras Lambda(X^{m,n}) for coprime integers m,n, each one isomorphic to the algebra of symmetric functions. Using a combinatorial construction, we identify certain rational functions that correspond to LLT polynomials in Lambda(X^{m,n}). As a corollary, we recover a raising operator formula for nabla applied to an LLT polynomial, special cases of which include nabla applied to Schur function and nabla applied to a Hall-Littlewood polynomial. This work is joint with Jonah Blasiak, Mark Haiman, Jennifer Morse, and Anna Pun. Speaker(s): George Seelinger (University of Michigan)
Building: East Hall
Event Type: Workshop / Seminar
Tags: Mathematics
Source: Happening @ Michigan from Department of Mathematics