A New Grounded Partition Identity of Type $D_4^{(3)}$
Combinatorics
2026-05-04 v5 Representation Theory
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 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.
Keywords
Cite
@article{arxiv.2410.21879,
title = {A New Grounded Partition Identity of Type $D_4^{(3)}$},
author = {Benedek Dombos},
journal= {arXiv preprint arXiv:2410.21879},
year = {2026}
}