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arXiv · 2111.10279

Partition identities from higher level crystals of $A_1^{(1)}$

Jehanne Dousse·Leonard Hardiman·Isaac Konan
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Abstract

We study perfect crystals for the standard modules of the affine Lie algebra $A_1^{(1)}$ 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.

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Jehanne Dousse, Leonard Hardiman, Isaac Konan. 2025-03-11. Partition identities from higher level crystals of $A_1^{(1)}$. https://doi.org/10.1090/proc%2F16417

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