Highest weight vectors of tensors

Abstract

We study highest weight vectors for symmetric and alternating spaces of tensors, whose dimensions are given by generalized Kronecker coefficients. We describe the algebraic relations for classical constructions of corresponding spanning sets of highest weight vectors. The proof is based on important duality that we discover for these highest weight spaces and vectors. As applications of duality, we also give conceptual interpretations to power expansions of Cayley's first hyperdeterminant and its dual exterior form.

Theorem 1.1 extended to all algebraic relations, Example 1.1 and several remarks are added. 40 pages, 2 figures