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Generalised Cartan invariants of symmetric groups


Author: Anton Evseev
Journal: Trans. Amer. Math. Soc. 367 (2015), 2823-2851
MSC (2010): Primary 20C30
DOI: https://doi.org/10.1090/S0002-9947-2014-06176-X
Published electronically: December 3, 2014
MathSciNet review: 3301883
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Abstract: Külshammer, Olsson, and Robinson developed an $ \ell $-analogue of modular representation theory of symmetric groups where $ \ell $ 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 version of the conjecture due to Bessenrodt and Hill.


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Additional Information

Anton Evseev
Affiliation: School of Mathematics, University of Birmingham, Edgbaston, Birmingham B15 2TT, United Kingdom
Email: A.Evseev@bham.ac.uk

DOI: https://doi.org/10.1090/S0002-9947-2014-06176-X
Received by editor(s): October 15, 2012
Received by editor(s) in revised form: May 1, 2013, and May 7, 2013
Published electronically: December 3, 2014
Additional Notes: The author was supported by the EPSRC Postdoctoral Fellowship EP/G050244/1.
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.