# The complexity of certain Specht modules for the symmetric group - Mathematics > Representation Theory

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Abstract: During the 2004-2005 academic year the VIGRE algebra research group at theUniversity of Georgia computed the complexities of certain Specht modulesS^\lambda for the symmetric group, using the computer algebra program Magma.The complexity of an indecomposable module does not exceed the p-rank of thedefect group of its block. The Georgia group conjectured that, generically, thecomplexity of a Specht module attains this maximal value; that it is smallerprecisely when the Young diagram of $\lambda$ is built out of $p \times p$blocks. We prove one direction of this conjecture by showing these Spechtmodules do indeed have less than maximal complexity. It turns out that thisclass of partitions, which has not previously appeared in the literature,arises naturally as the solution to a question about the $p$-weight ofpartitions and branching.

Author: ** David J. Hemmer**

Source: https://arxiv.org/