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Decomposing symmetric powers of certain modular representations of cyclic groups

R. J. Shank·D. L. Wehlau
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Abstract

For a prime number p, we construct a generating set for the ring of invariants for the p+1 dimensional indecomposable modular representation of a cyclic group of order p^2. We then use the constructed invariants to describe the decomposition of the symmetric algebra as a module over the group ring, confirming the Periodicity Conjecture of Ian Hughes and Gregor Kemper for this case.

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R. J. Shank, D. L. Wehlau. 2007-05-29. Decomposing symmetric powers of certain modular representations of cyclic groups. https://arxiv.org/abs/math/0509044

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