Tensor fundamental theorems of invariant theory

Abstract

The aim of this paper is to establish a first and second fundamental theorem for G L ( V ) GL(V) equivariant polynomial maps from k k –tuples of matrix variables E n d ( V ) k End(V)^{ k} to tensor spaces E n d ( V ) ⊗ n End(V)^{ \otimes n} , in the spirit of H. Weyl’s book The Classical Groups and of symbolic algebra.