Vol. 7, No. 1, 2015

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Free resolutions and modules with a semisimple Lie group action

Federico Galetto

Vol. 7 (2015), 17–29
Abstract

We introduce the package HighestWeights for Macaulay2. This package provides tools to study the representation-theoretic structure of free resolutions and graded modules over a polynomial ring with the action of a semisimple Lie group. The methods of this package allow users to consider the free modules in a resolution, or the graded components of a module, as representations of a semisimple Lie group by means of their weights, and to obtain their decomposition into highest-weight representations.

Keywords
equivariant free resolution, irreducible representation, highest weight, algebraic torus, semisimple Lie group, decomposition algorithm
Mathematical Subject Classification 2010
Primary: 13P20
Secondary: 22E46
Supplementary material

HighestWeights version 0.6.5

Milestones
Received: 11 July 2014
Revised: 23 August 2014
Accepted: 5 June 2015
Published: 5 July 2015
Authors
Federico Galetto
Department of Mathematics and Statistics
Queen’s University
48 University Avenue
Kingston K7L 3N6
Canada