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On the Endomorphism Algebra of Specht Modules in Even Characteristic (2301.12582v2)
Published 29 Jan 2023 in math.RT
Abstract: Over fields of characteristic $2$, Specht modules may decompose and there is no upper bound for the dimension of their endomorphism algebra. A classification of the (in)decomposable Specht modules and a closed formula for the dimension of their endomorphism algebra remain two important open problems in the area. In this paper, we introduce a novel description of the endomorphism algebra of the Specht modules and provide infinite families of Specht modules with one-dimensional endomorphism algebra.