Treffer: Partition identities from higher level crystals of 𝐴₁⁽¹⁾: Partition identities from higher level crystals of \(A_1^{(1)}\)

Title:
Partition identities from higher level crystals of 𝐴₁⁽¹⁾: Partition identities from higher level crystals of \(A_1^{(1)}\)
Authors:
Dousse, Jehanne, Hardiman, Leonard, Konan, Isaac
Source:
Proceedings of the American Mathematical Society. 153:1363-1382
Publication Status:
Preprint
Publisher Information:
American Mathematical Society (AMS), 2025.
Publication Year:
2025
Subject Terms:
Representations of Lie algebras and Lie superalgebras, algebraic theory (weights), Exact enumeration problems, generating functions, Rogers-Ramanujan-type identities, 01 natural sciences, crystal bases, Partition identities, identities of Rogers-Ramanujan type, Mathematics - Quantum Algebra, FOS: Mathematics, Infinite-dimensional Lie (super)algebras, Mathematics - Combinatorics, Quantum Algebra (math.QA), Number Theory (math.NT), 0101 mathematics, Representation Theory (math.RT), Combinatorial identities, bijective combinatorics, Combinatorial aspects of partitions of integers, Mathematics - Number Theory, Elementary theory of partitions, character formulas, Kac-Moody (super)algebras, extended affine Lie algebras, toroidal Lie algebras, 05A15, 05A17, 05A30, 05E10, 11P81, 11P84, 17B10, 17B65, 17B67, Kac-Moody Lie algebras, integer partitions, Combinatorial aspects of representation theory, Combinatorics (math.CO), Mathematics - Representation Theory
Document Type:
Fachzeitschrift Article
File Description:
application/xml
Language:
English
ISSN:
1088-6826
0002-9939
DOI:
10.1090/proc/16417
DOI:
10.48550/arxiv.2111.10279
Access URL:
http://arxiv.org/abs/2111.10279
https://zbmath.org/7991239
https://doi.org/10.1090/proc/16417
Rights:
arXiv Non-Exclusive Distribution
URL: https://www.ams.org/publications/copyright-and-permissions
Accession Number:
edsair.doi.dedup.....10dc5387e1a1f1b20805795d6e2751af
Database:
OpenAIRE

Weitere Informationen

We study perfect crystals for the standard modules of the affine Lie algebra A 1 ( 1 ) A_1^{(1)} at all levels using the theory of multi-grounded partitions. We prove a family of partition identities which are reminiscent of the Andrews–Gordon identities and companions to the Meurman–Primc identities, but with simple difference conditions involving absolute values.