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The Tilting Tensor Product Theorem and Decomposition Numbers for Symmetric Groups

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Abstract

We show how the tilting tensor product theorem for algebraic groups implies a reduction formula for decomposition numbers of the symmetric group. We use this to prove generalisations of various theorems of Erdmann and of James and Williams.

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  1. Centre for Mathematical Science, City University, Northampton Square, London, EC1V 0HB, England

    Anton Cox

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  1. Anton Cox
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Correspondence to Anton Cox.

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Supported by Nuffield grant scheme NUF-NAL 02. Preliminary work on this paper was undertaken at the Isaac Newton Institute as part of the programme on Symmetric Functions and Macdonald Polynomials.

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Cox, A. The Tilting Tensor Product Theorem and Decomposition Numbers for Symmetric Groups. Algebr Represent Theor 10, 307–314 (2007). https://doi.org/10.1007/s10468-007-9051-8

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