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This content will become publicly available on June 26, 2026

Title: Super major index and Thrall’s problem
Thrall’s problem asks for the Schur decomposition of the higher Lie modules $$L_\lambda$$, which are defined using the free Lie algebra and decompose the tensor algebra as a general linear group module. Although special cases have been solved, Thrall’s problem remains open in general. We generalize Thrall’s problem to the free Lie superalgebra, and prove extensions of three known results in this setting: Brandt’s formula, Klyachko’s identification of the Schur–Weyl dual of $$L_n$$, and Kráskiewicz–Weyman’s formula for the Schur decomposition of $$L_n$$. The latter involves a new version of the major index on super tableaux, which we show corresponds to a $q,t$-hook formula of Macdonald.  more » « less
Award ID(s):
2348843
PAR ID:
10626828
Author(s) / Creator(s):
;
Publisher / Repository:
Algebraic Combinatorics
Date Published:
Journal Name:
Algebraic Combinatorics
Volume:
8
Issue:
3
ISSN:
2589-5486
Page Range / eLocation ID:
795 to 815
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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