LAUSR

Abstract 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 m W ⊕ d W ⁎ 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 } ⊆ F q [ m W ⊕ d W ⁎ ] G such that F q ( m W ⊕ d W ⁎ ) G = F q ( l 1 , l 2 , … , l ( m + d ) n ) for all cases except when m d = 0 and G = GL ( n , F q ) or SL ( n , F q ) .