Decomposing Symmetric Powers of Certain Modular Representations of Cyclic Groups

@article{Shank2005DecomposingSP,
  title={Decomposing Symmetric Powers of Certain Modular Representations of Cyclic Groups},
  author={R. James Shank and David L. Wehlau},
  journal={arXiv: Commutative Algebra},
  year={2005},
  pages={169-196}
}
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, and show that the Noether number for the representation is p 2 + p−3. We then use the constructed invariants to explicitly 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. In the final section, we use our… 

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