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

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- by Matthew Fayers PDF
- Trans. Amer. Math. Soc.
**360**(2008), 1341-1376 Request permission

## 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

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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
- 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
- © Copyright 2007 American Mathematical Society
- 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
- MathSciNet review: 2357698