Partition identities from higher level crystals of 𝐴₁⁽¹⁾

Dousse, Jehanne; Hardiman, Leonard; Konan, Isaac

doi:10.1090/proc/16417

Partition identities from higher level crystals of $A_1^{(1)}$
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by Jehanne Dousse, Leonard Hardiman and Isaac Konan;

Proc. Amer. Math. Soc. 153 (2025), 1363-1382

DOI: https://doi.org/10.1090/proc/16417

Published electronically: February 5, 2025

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