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LLT polynomials in the Schiffmann algebra.
- Source :
-
Journal für die Reine und Angewandte Mathematik . Jun2024, Vol. 2024 Issue 811, p93-133. 41p. - Publication Year :
- 2024
-
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]
Details
- Language :
- English
- ISSN :
- 00754102
- Volume :
- 2024
- Issue :
- 811
- Database :
- Academic Search Index
- Journal :
- Journal für die Reine und Angewandte Mathematik
- Publication Type :
- Academic Journal
- Accession number :
- 177519738
- Full Text :
- https://doi.org/10.1515/crelle-2024-0012