The complexity of certain Specht modules for the symmetric group |
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Authors: | David J Hemmer |
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Institution: | 1.Department of Mathematics,University at Buffalo, SUNY,Buffalo,USA |
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Abstract: | During the 2004–2005 academic year the VIGRE Algebra Research Group at the University of Georgia (UGA VIGRE) computed the
complexities of certain Specht modules S
λ
for the symmetric group Σ
d
, using the computer algebra program Magma. The complexity of an indecomposable module does not exceed the p-rank of the defect group of its block. The UGA VIGRE Algebra Group conjectured that, generically, the complexity of a Specht
module attains this maximal value; that it is smaller precisely when the Young diagram of λ is built out of p×p blocks. We prove one direction of this conjecture by showing these Specht modules do indeed have less than maximal complexity.
It turns out that this class of partitions, which has not previously appeared in the literature, arises naturally as the solution
to a question about the p-weight of partitions and branching. |
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Keywords: | |
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