The heights of irreducible Brauer characters in 2-blocks of the symmetric groups

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Abstract

We prove that there exists a unique irreducible Brauer character of height zero in any 2-blocks of the symmetric group. This generalizes the theorem of P. Fong and G.D. James that the dimension of every non-trivial 2-modular simple module of the symmetric group is even. © 2012 Elsevier Inc.

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Kiyota, M., Okuyama, T., & Wada, T. (2012). The heights of irreducible Brauer characters in 2-blocks of the symmetric groups. Journal of Algebra, 368, 329–344. https://doi.org/10.1016/j.jalgebra.2012.07.001

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