English

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 A1(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.

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