Multi-grounded partitions and character formulas

DOI10.1016/J.AIM.2022.108275arXiv2103.04983WikidataQ113880988 ScholiaQ113880988MaRDI QIDQ6362424

Isaac Konan, Jehanne Dousse

Publication date: 8 March 2021

Abstract: 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 $A_{2n}^{(2)}(ngeq2)$, $D_{n+1}^{(2)}(ngeq2)$, $A_{2n-1}^{(1)}(ngeq3)$, $B_n^{(1)}(ngeq3)$, and $D_n^{(1)}(ngeq4)$.

Mathematics Subject Classification ID

Combinatorial aspects of partitions of integers (05A17) Combinatorial aspects of representation theory (05E10) Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Elementary theory of partitions (11P81)

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