Schur apolarity. (January 2023)

• Record Type: Journal Article
• Authors: Staffolani, Reynaldo
• Is Part Of: Journal of symbolic computation. Volume 114(2023)
• Page Start: 37
• Page End: 73
• Publication Date: 2023-01
• Subjects: Tensor decomposition -- Secant variety -- Schur functor -- Multilinear algebra; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2022.04.017
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: Inspired by the classic apolarity theory of symmetric tensors, the aim of this paper is to introduce the Schur apolarity theory, i.e. an apolarity for any irreducible representation of the special linear group S L ( V ) . This allows to describe decompositions of structured tensors whose elementary elements are tensors that represent flags of the vector space V . The main result is the Schur apolarity lemma which is the analogous of the apolarity lemma of symmetric apolarity theory. Eventually we study the rank tensors of low border rank related to specific varieties giving rise also to simple algorithms.