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arXiv · 2608.13661

Specht Modules With Trivial Direct Summands

David J. Hemmer
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Abstract

We prove that, in characteristic $2$, a Specht module indexed by a nonhook partition cannot have a trivial direct summand. The proof uses the KLR grading and a recent graded homomorphism theorem of Hudak. Together with Murphy's theorem for hooks, this gives the complete classification of trivial direct summands of Specht modules in characteristic $2$, answering a question posed by Collins--Dodge and Dodge--Van Vlack.

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David J. Hemmer. 2026-08-13. Specht Modules With Trivial Direct Summands. https://arxiv.org/abs/2608.13661

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