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Rings of invariants for three dimensional modular representations

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Abstract

Let \(p>3\) be a prime number. We compute the rings of invariants of the elementary abelian p-group \(({{\mathbb {Z}}}/p{{\mathbb {Z}}})^r\) for 3-dimensional generic representations. Furthermore we show that these rings of invariants are complete intersection rings with embedding dimension \(\lceil r/2\rceil +3\). This proves a conjecture of Campbell, Shank and Wehlau in [CSW], which they proved for \(r=3\), and was later proved for \(r=4\) by Pierron and Shank.

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Authors and Affiliations

  1. Fakultät für Mathematik, Universität Duisburg-Essen, 45117, Essen, Germany

    Jürgen Herzog

  2. School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai, 400005, India

    Vijaylaxmi Trivedi

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  1. Jürgen Herzog
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  2. Vijaylaxmi Trivedi
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Correspondence to Vijaylaxmi Trivedi.

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The second author acknowledges support of the Department of Atomic Energy, India under project number RTI4001.

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Herzog, J., Trivedi, V. Rings of invariants for three dimensional modular representations. Math. Z. 305, 22 (2023). https://doi.org/10.1007/s00209-023-03350-2

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