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Manuscripta Mathematica

, Volume 144, Issue 3–4, pp 341–348 | Cite as

On modular invariants of a vector and a covector

  • Yin ChenEmail author
Article

Abstract

Let GL 2(F q ) be the general linear group over a finite field F q , V be the 2-dimensional natural representation of GL 2(F q ) and V * be the dual representation. We denote by \({F_{q}[V\oplus V^{\ast}]^{GL_{2}(F_{q})}}\) the corresponding invariant ring of a vector and a covector for GL 2(F q ). In this paper, we prove that \({F_{q}[V\oplus V^{\ast}]^{GL_{2}(F_{q})}}\) is a Gorenstein algebra. This result confirms a special case (n = 2) of the recent conjecture of Bonnafé and Kemper (J Algebra 335:96–112, 2011).

Mathematics Subject Classification (1991)

13A50 20H30 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsNortheast Normal UniversityChangchunPeople’s Republic of China
  2. 2.Chern Institute of MathematicsNankai UniversityTianjinPeople’s Republic of China

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