Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Decomposition numbers for weight three blocks of symmetric groups and Iwahori-Hecke algebras


Author: Matthew Fayers
Journal: Trans. Amer. Math. Soc. 360 (2008), 1341-1376
MSC (2000): Primary 20C30, 20C08
Published electronically: October 16, 2007
MathSciNet review: 2357698
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Abstract: Let $ \mathbb{F}$ be a field, $ q$ a non-zero element of $ \mathbb{F}$ and $ \mathcal{H}_{n}=\mathcal{H}_{\mathbb{F},q}(\mathfrak{S}_n)$ the Iwahori-Hecke algebra of the symmetric group $ \mathfrak{S}_n$. If $ B$ is a block of $ \mathcal{H}_{n}$ of $ e$-weight $ 3$ and the characteristic of $ \mathbb{F}$ is at least $ 5$, we prove that the decomposition numbers for $ B$ are all at most $ 1$. In particular, the decomposition numbers for a $ p$-block of $ \mathfrak{S}_n$ of defect $ 3$ are all at most $ 1$.


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Additional Information

Matthew Fayers
Affiliation: School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London E1 4NS, United Kingdom

DOI: http://dx.doi.org/10.1090/S0002-9947-07-04156-6
Received by editor(s): April 12, 2004
Received by editor(s) in revised form: July 28, 2005, and September 29, 2005
Published electronically: October 16, 2007
Additional Notes: An earlier version of this paper was written while the author was a research fellow at Magdalene College, Cambridge
Article copyright: © Copyright 2007 American Mathematical Society