On invariant fields of vectors and covectors

摘要

Let F-q be the finite field of order q. Let G be one of the three groups GL(n, F-q), SL(n, F-q) or U(n, F-q) and let W be the standard n-dimensional representation of G. For non-negative integers m and d we let mW circle plus dW* denote the representation of G given by the direct sum of m vectors and d covectors. We exhibit a minimal set of homogeneous invariant polynomials {l(1), l(2), ..., l((m+d)n)} subset of F-q[mW circle plus dW*](G) such that F-q(mW circle plus dW*)(G) = F-q (l(1), l(2), ..., l((m+d)n)) for all cases except when md = 0 and G = CL(n, F-q) or SL(n, F-q). Crown Copyright (C) 2018 Published by Elsevier B.V. All rights reserved.