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Transformation Groups

, Volume 18, Issue 1, pp 1–22 | Cite as

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

  • H. E. A. Campbell
  • R. J. Shank
  • D. L. Wehlau
Article

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.

Keywords

Complete Intersection Group Homomorphism Polynomial Algebra Left Action Modular Representation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • H. E. A. Campbell
    • 1
  • R. J. Shank
    • 2
  • D. L. Wehlau
    • 3
  1. 1.Department of MathematicsUniversity of New BrunswickFredrictonCanada
  2. 2.School of Mathematics, Statistics and Actuarial ScienceUniversity of KentCanterburyUK
  3. 3.Department of Mathematics and Computer ScienceRoyal Military CollegeKingstonCanada

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