A new grounded partition identity of type D₄⁽³⁾

2024/10/29 by Dombos, Benedek
#Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2410.21879

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⁾ 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.

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