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Journal article
LLT polynomials in the Schiffmann algebra
Journal für die reine und angewandte Mathematik, 2024
23 Apr 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 Lambda (X-m,X-n ) subset of 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 del operator applied to any LLT polynomial. In particular, we obtain a formula for backward difference del(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 Blasiak - Drexel UniversityMark Haiman - University of California, BerkeleyJennifer Morse - University of VirginiaAnna Pun - Baruch CollegeGeorge H. Seelinger - University of Michigan
- Publication Details
- Journal für die reine und angewandte Mathematik, 2024
- Publisher
- Walter De Gruyter
- Number of pages
- 41
- Grant note
- National Science Foundation; National Science Foundation (NSF)
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:001206854600001
- Scopus ID
- 2-s2.0-85191394123
- Other Identifier
- 991021874415504721
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- Collaboration types
- Domestic collaboration
- Web of Science research areas
- Mathematics