1. LLT polynomials in the Schiffmann algebra.
- Author
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Blasiak, Jonah, Haiman, Mark, Morse, Jennifer, Pun, Anna, and Seelinger, George H.
- Subjects
ALGEBRA ,FUNCTION algebras ,POLYNOMIALS ,ELLIPTIC functions ,ISOMORPHISM (Mathematics) ,SYMMETRIC functions - Abstract
We identify certain combinatorially defined rational functions which, under the shuffle to Schiffmann algebra isomorphism, map to LLT polynomials in any of the distinguished copies Λ (X m , n) ⊂ E of the algebra of symmetric functions embedded in the elliptic Hall algebra ℰ of Burban and Schiffmann. As a corollary, we deduce an explicit raising operator formula for the ∇ operator applied to any LLT polynomial. In particular, we obtain a formula for ∇ m s λ which serves as a starting point for our proof of the Loehr–Warrington conjecture in a companion paper to this one. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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