Generalised Cartan invariants of symmetric groups

2012/10/09 by Anton Evseev, Evseev, Anton
Mathematics · #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT) #math.GR #math.RT

paper · pdf · doi:10.48550/arxiv.1210.2679

Proofs simplified and proof of Lemma 3.8 corrected following referee's comments. To appear in Trans. Amer. Math. Soc

arxiv created 2013/07/15 · arxiv updated 2013/07/16

Abstract

Külshammer, Olsson, and Robinson developed an l-analogue of modular representation theory of symmetric groups where l is not necessarily a prime. They gave a conjectural combinatorial description for invariant factors of the Cartan matrix in this context. We confirm their conjecture by proving a more precise blockwise conjecture due to Bessenrodt and Hill.

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