Séminaire Lotharingien de Combinatoire, 93B.38 (2025), 12 pp.

Sam Armon and Joshua P. Swanson

On a Super vVrsion of Thrall's Problem

Abstract. Thrall's problem asks for the irreducible decompositions of the Lie modules Lλ, which decompose the tensor algebra as a general linear group module. In this extended abstract of \cite{ArS}, we describe a super generalization of Thrall's problem and develop new super tableau combinatorics in order to extend known results to this new setting. As a sample of our results, we obtain a combinatorial interpretation of a q,t-hook formula of Macdonald.


Received: November 15, 2024. Accepted: February 15, 2025. Final version: April 1, 2025.

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