Decomposing symmetric powers of certain modular representations of cyclic groups
Commutative Algebra
2007-06-13 v2 Representation Theory
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.
Keywords
Cite
@article{arxiv.math/0509044,
title = {Decomposing symmetric powers of certain modular representations of cyclic groups},
author = {R. J. Shank and D. L. Wehlau},
journal= {arXiv preprint arXiv:math/0509044},
year = {2007}
}
Comments
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