# Rings of invariants for modular representations of elementary abelian p-groups

Campbell, Eddy, Shank, R. James, Wehlau, David L. (2013) Rings of invariants for modular representations of elementary abelian p-groups. Transformation Groups, 18 (1). pp. 1-22. ISSN 1083-4362 (online 1531-586X). (doi:10.1007/s00031-013-9207-z) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided) (KAR id:33288)

 The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided. (Contact us about this Publication) Official URLhttp://dx.doi.org/10.1007/s00031-013-9207-z

## Abstract

We initiate a study of the rings of invariants of modular representations of elementary abelian $p$-groups. With a few notable exceptions, the modular representation theory of an elementary abelian $p$-group is wild. However, for a given dimension, it is possible to parameterise the representations. We describe parameterisations for modular representations of dimension two and of dimension three. We compute the ring of invariants for all two dimensional representations; these

rings are generated by two algebraically independent elements. We compute the ring of invariants of the symmetric square of a two dimensional representation; these rings are hypersurfaces. We compute the ring of invariants for all three dimensional representations of rank at most three; these rings are complete intersections with embedding dimension at most five. We conjecture that the ring of invariants for any three dimensional representation of an elementary abelian $p$-group is a complete intersection.

Item Type: Article 10.1007/s00031-013-9207-z modular invariant theory Q Science > QA Mathematics (inc Computing science) > QA150 Algebra Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Pure Mathematics James Shank 01 Mar 2013 12:46 UTC 06 May 2020 03:07 UTC https://kar.kent.ac.uk/id/eprint/33288 (The current URI for this page, for reference purposes) https://orcid.org/0000-0002-3317-4088