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

TL;DR

This paper introduces a new Rogers-Ramanujan-type identity related to grounded partitions by analyzing the affine Kac-Moody algebra D_4^{(3)} through two distinct methods.

Contribution

It presents a novel identity for grounded partitions derived from affine Kac-Moody algebra D_4^{(3)} using character computations with two different approaches.

Findings

Derived a new Rogers-Ramanujan-type identity involving grounded partitions.

Connected the identity to the character of the affine Kac-Moody algebra D_4^{(3)}.

Utilized Lepowsky's product formula and crystal techniques for the derivation.

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.