Generalised Cartan invariants of symmetric groups
Representation Theory
2013-07-16 v3 Group Theory
Abstract
K\"ulshammer, 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.
Keywords
Cite
@article{arxiv.1210.2679,
title = {Generalised Cartan invariants of symmetric groups},
author = {Anton Evseev},
journal= {arXiv preprint arXiv:1210.2679},
year = {2013}
}
Comments
Proofs simplified and proof of Lemma 3.8 corrected following referee's comments. To appear in Trans. Amer. Math. Soc