Multi-grounded partitions and character formulas - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2021

Multi-grounded partitions and character formulas

Résumé

We introduce a new generalisation of partitions, multi-grounded partitions, related to ground state paths indexed by dominant weights of Lie algebras. We use these to express characters of irreducible highest weight modules of Kac-Moody algebras of affine type as generating functions for multi-grounded partitions. This generalises the approach of our previous paper, where only irreducible highest weight modules with constant ground state paths were considered, to all ground state paths. As an application, we compute the characters of the level $1$ modules of the affine Lie algebras $A_{2n}^{(2)}(n\geq 2)$, $D_{n+1}^{(2)}(n\geq 2)$, $A_{2n-1}^{(1)}(n\geq 3)$, $B_{n}^{(1)}(n\geq 3)$, and $D_{n}^{(1)}(n\geq 4)$.

Dates et versions

hal-03448455 , version 1 (25-11-2021)

Identifiants

Citer

Jehanne Dousse, Isaac Konan. Multi-grounded partitions and character formulas. 2021. ⟨hal-03448455⟩
17 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More