Propagating weights of tori along free resolutions. (May 2016)

• Record Type: Journal Article
• Authors: Galetto, Federico
• Is Part Of: Journal of symbolic computation. Volume 74(2016)
• Page Start: 1
• Page End: 45
• Publication Date: 2016-05
• Subjects: primary 13D02 -- secondary 13A50 13P20 20G05; Equivariant free resolution -- Irreducible representation -- Weight -- Torus -- Reductive group -- Algorithm; 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.2015.05.004
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: The action of a torus on a graded module over a polynomial ring extends to the entire minimal free resolution of the module. We explain how to determine the action of the torus on the free modules in the resolution, when the resolution can be calculated explicitly. The problem is reduced to analyzing how the weights of a torus propagate along an equivariant map of free modules. The results obtained are used to design algorithms which have been implemented in the software system Macaulay2.