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

Kai Meng Tan
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Abstract

We prove that the v-decomposition number $d_{λμ}(v)$ is an even or odd polynomial according to whether the partitions $λ$ and $μ$ 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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BibTeXRIS

Kai Meng Tan. 2006-09-05. Parities of v-decomposition numbers and an application to symmetric group algebras. https://arxiv.org/abs/math/0606460

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