Partition identities from higher level crystals of $A_1^{(1)}$
Combinatorics
2025-03-12 v2 Number Theory
Quantum Algebra
Representation Theory
Abstract
We study perfect crystals for the standard modules of the affine Lie algebra 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.
Keywords
Cite
@article{arxiv.2111.10279,
title = {Partition identities from higher level crystals of $A_1^{(1)}$},
author = {Jehanne Dousse and Leonard Hardiman and Isaac Konan},
journal= {arXiv preprint arXiv:2111.10279},
year = {2025}
}
Comments
15 pages, 2 figures; v2: multiple minor changes suggested during the refereeing process