English

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 D4(3)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.

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}
}