Remote Access Transactions of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9947-07-04156-6
Published electronically: October 16, 2007
MathSciNet review: 2357698
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 $1$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 20C30, 20C08

Retrieve articles in all journals with MSC (2000): 20C30, 20C08


Additional Information

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

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