Work

Schur apolarity

Year: 2021

Type: preprint

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 $SL(V)$. 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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2109.12695

Author: Staffolani, Reynaldo

Language: English

Topic: Tensor decomposition and applications

Subfield: Computational Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Università degli Studi di Trento, Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni

OpenAlex ID: W4294769644

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