A Galois correspondence for reductive groups and applications to the First Fundamental Theorems

Following some unpublished ideas of Lex Schrijver we will explain a new approach to the First Fundamental Theorems (FFTs) from classical invariant theory. It uses the tensor product of the two tensor algebras $T(V)$ and $T(V^*)$ with the aim to set up a Galois correspondence between reductive subgroups of GL(V) and certain subalgebras. As a consequence, one gets -- in a unified way -- the well-known FFTs for the classical groups and -- in addition -- also new FFTs for other groups.