Skip to content
DSML.KZ
Publications

Preprint · arXiv · April 21, 2025

Highest weight vectors of tensors

Alimzhan Amanov, Damir Yeliussizov

Alimzhan Amanov
Read on arXivPDFDOI 10.48550/arxiv.2504.15413

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.

Advanced Combinatorial MathematicsTensor decomposition and applicationsAdvanced Algebra and Geometryhighest weight vectorstensorssymmetric tensors

More by Alimzhan Amanov