2010/06/24 by Cédric Bonnafé, Gregor Kemper, Bonnafé, Cédric +2
Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Finite Group Theory Research #math.AC #math.AG
paper · pdf · doi:10.48550/arxiv.1006.4762
16 pages
arxiv created 2011/04/04 · arxiv updated 2011/04/05
Given a linear action of a group G on a K-vector space V, we consider the invariant ring K[V ⊕ V^*]G, where V^* is the dual space. We are particularly interested in the case where V =\gfqn and G is the group Un of all upper unipotent matrices or the group Bn of all upper triangular matrices in \GLn(\gfq). In fact, we determine \gfq[V ⊕ V^*]G for G = Un and G =Bn. The result is a complete intersection for all values of n and q. We present explicit lists of generating invariants and their relations. This makes an addition to the rather short list of "doubly parametrized" series of group actions whose invariant rings are known to have a uniform description.