SIGMA 22 (2026), 042, 17 pages      arXiv:2410.21879      https://doi.org/10.3842/SIGMA.2026.042
Contribution to the Special Issue on Recent Advances in Vertex Operator Algebras in honor of James Lepowsky

A New Grounded Partition Identity of Type $D_4^{(3)}$

Benedek Dombos
Section de mathématiques, Université de Genève, Switzerland

Received December 18, 2025, in final form April 19, 2026; Published online April 30, 2026

Abstract
In this paper, we prove a new Rogers-Ramanujan-type identity, involving grounded partitions, by computing a character of the affine Kac-Moody algebra $D_4^{(3)}$ in two different ways. The product side is derived using Lepowsky's product formula, while the sum side is obtained using perfect crystals with a technique of Dousse and Konan.

Key words: grounded partitions; Rogers-Ramanujan-type identities; perfect crystals; affine Kac-Moody algebras; principal specialisation.

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