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HighestWeights -- decompose free resolutions and graded modules with a semisimple Lie group action

Description

This package provides tools to study the representation theoretic structure of equivariant free resolutions and graded modules with the action of a semisimple Lie group. The methods of this package allow one to consider the free modules in an equivariant 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.

This package implements an algorithm introduced in Galetto - Propagating weights of tori along free resolutions. The methods of this package are meant to be used in characteristic zero.

The following links contain some sample computations carried out using this package. The first and second example are discussed in more detail, so we recommend reading through them first.

Author

Certification a gold star

Version 0.6.5 of this package was accepted for publication in volume 7 of The Journal of Software for Algebra and Geometry on 5 June 2015, in the article Free resolutions and modules with a semisimple Lie group action (DOI: 10.2140/jsag.2015.7.9). That version can be obtained from the journal.

Version

This documentation describes version 0.6.5 of HighestWeights.

Citation

If you have used this package in your research, please cite it as follows:

@misc{HighestWeightsSource,
  title = {{HighestWeights: A \emph{Macaulay2} package. Version~0.6.5}},
  author = {Federico Galetto},
  howpublished = {A \emph{Macaulay2} package available at
    \url{https://github.com/Macaulay2/M2/tree/master/M2/Macaulay2/packages}}
}

@article{HighestWeightsArticle,
  title = {{Free resolutions and modules with a semisimple Lie group action}},
  author = {Federico Galetto},
  journal = {The Journal of Software for Algebra and Geometry},
  volume = {7},
  year = {2015},
}

Exports

For the programmer

The object HighestWeights is a package, defined in HighestWeights.m2, with auxiliary files in HighestWeights/.


The source of this document is in HighestWeights/doc.m2:55:0.