Generalised Cartan invariants of symmetric groups

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.

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