Decomposition numbers for symmetric groups

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Where to find decomposition matrices? Try www.math.rwth-aachen.de/∼MOC In hard copy, [6] has several (at the end) for small primes. For p = 2, a paper by Juergen Mueller(Aachen) [7], for an electronic version try his homepage. General background can be found in [6]. Column removal: Due to G.D. James, sometime after '76. Just now I cannot find the precise reference. However, a generalization of the various removals has recently been done by Fayers and Lyle [3]. A reference to the original should be in there. Two-part partitions: The original paper is [5], it is just for p = 2. The odd prime paper is slightly later (again, I cannot find the reference just now). But there is not much in it, he just says 'it's the same as p = 2. His proof is quite long. There is now a short proof, due to S. Donkin, using new technology. This can be found in [1], the last chapter. More on fractal structure of decomposition matrices for 2-part partitions can be found in [4]. Blocks. The result by Scopes (including details with the abacus) is in [8]. The decomposition map: The details are in the paper [2]. to be added reference for the number of simples in a p-block of weight w. Maybe in [8] there is a reference? References [1] K. Erdmann, Symmetric groups and quasi-hereditary algebras. in Finite dimensional algebras and related topics, ed V.

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تاریخ انتشار 2009