# Decomposing symmetric powers of certain modular representations of cyclic groups

Shank, R. James and Wehlau, David L. (2009) Decomposing symmetric powers of certain modular representations of cyclic groups. In: Campbell, Eddy and Helminck, Aloysius G. and Kraft, Hanspeter and Wehlau, David L., eds. Symmetry and Spaces: In Honor of Gerry Schwarz. Progress in Mathematics, 278 . Birkhauser, Berlin, pp. 169-196. ISBN 978-0-8176-4874-9 (Print) 978-0-8176-4875-6 (Online). (doi:10.1007/978-0-8176-4875-6_9)

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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.

Item Type: Book section 10.1007/978-0-8176-4875-6_9 The revised version of the paper includes a calculation of the Noether number of the p+1 dimensional modular indecomposable representation of the cyclic group of order p^2 and the Hilbert series of the corresponding ring of invariants Q Science > QA Mathematics (inc Computing science) > QA150 Algebra Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Pure Mathematics R James Shank 06 Jun 2008 17:15 UTC 28 May 2019 13:38 UTC https://kar.kent.ac.uk/id/eprint/3169 (The current URI for this page, for reference purposes)