• DOI:10.1007/978-0-8176-4875-6_9
• Corpus ID: 1515305

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}
}

• R. Shank, D. Wehlau
• Published 2 September 2005
• Mathematics
• arXiv: Commutative Algebra

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 results to compute the Hilbert series for the corresponding ring of invariants together with some other related generating functions.