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Preprint
LLT polynomials in the Schiffmann algebra
arXiv (Cornell University)
13 Dec 2021
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 $\Lambda (X^{m,n})\subset \mathcal{E}$ of the algebra
of symmetric functions embedded in the elliptic Hall algebra $\mathcal{E}$ of
Burban and Schiffmann. As a corollary, we deduce an explicit raising operator
formula for the $\nabla$ operator applied to any LLT polynomial. In particular,
we obtain a formula for $\nabla ^m s_\lambda$ which serves as a starting point
for our proof of the Loehr-Warrington conjecture in a companion paper to this
one.
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Details
- Title
- LLT polynomials in the Schiffmann algebra
- Creators
- Jonah BlasiakMark HaimanJennifer MorseAnna PunGeorge Seelinger
- Publication Details
- arXiv (Cornell University)
- Resource Type
- Preprint
- Language
- English
- Academic Unit
- Mathematics
- Other Identifier
- 991021862386204721