Parities of v-decomposition numbers and an application to symmetric group algebras

Details Parities of v-decomposition numbers and an application to symmetric group algebras Parities of v-decomposition numbers and an application to symmetric group algebras

2006-06-19

arxiv.org/abs/math/0606460v2

Mathematics

Representation Theory

21 pages

Scientific paper

We prove that the v-decomposition number $d_{\lambda\mu}(v)$ is an even or odd polynomial according to whether the partitions $\lambda$ and $\mu$ have the same relative sign (or parity) or not. We then use this result to verify Martin's conjecture for weight 3 blocks of symmetric group algebras -- that these blocks have the property that their projective (indecomposable) modules have a common radical length 7.

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