Modular invariants of a vector and a covector for some elementary abelian p-groups

Abstract

Let F p be the prime field of order p > 0 and G be an elementary abelian p-group. For some n-dimensional cohyperplane G-representations V over F p , we show that F p [ V ⊕ V * ] G , the invariant ring of a vector and a covector is a complete intersection by exhibiting an explicit generating set (in fact, a SAGBI basis) and exposing all relations among the generators.