SchurComplexes -- Schur functors of chain complexes

Description

This package computes the Schur complex $S_{\lambda}F_{\bullet}$ associated to a bounded chain complex $F_{\bullet}$ of finitely-generated free modules, and a partition $\lambda$. Our conventions are the transpose of the convention in "Cohomology of Vector Bundles and Syzygies", by Jerzy Weyman, Chapter 2.4.

Authors

Certification

Version 1.1 of this package was accepted for publication in volume 9 of Journal of Software for Algebra and Geometry on 21 August 2019, in the article Computing Schur complexes (DOI: 10.2140/jsag.2019.9.111). That version can be obtained from the journal.

Version

This documentation describes version 1.1 of SchurComplexes.

Citation

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

@misc{SchurComplexesSource,
  title = {{SchurComplexes: Schur functors of complexes. Version~1.1}},
  author = {Michael K. Brown and Amy Huang and Robert Laudone and Michael Perlman and Claudiu Raicu and Steven V Sam and Joao Pedro Santos},
  howpublished = {A \emph{Macaulay2} package available at
    \url{https://github.com/Macaulay2/M2/tree/master/M2/Macaulay2/packages}}
}

@article{SchurComplexesArticle,
  title = {{Computing Schur complexes}},
  author = {Michael K. Brown and Amy Huang and Robert Laudone and Michael Perlman and Claudiu Raicu and Steven V Sam and Joao Pedro Santos},
  journal = {Journal of Software for Algebra and Geometry},
  volume = {9},
  year = {2019},
}

Exports

Functions and commands
- schurComplex -- Schur functors of chain complexes
- straightenTableau -- Straightening law for Z/2Z-graded tableau

For the programmer

The object SchurComplexes is a package, defined in SchurComplexes.m2.

The source of this document is in SchurComplexes.m2:456:0.