WeylGroups

This is the homepage of the Macaulay 2 package WeylGroups, written by Baptiste Calmès and Viktor Petrov, and dedicated to all sorts of computations involving root systems, Weyl groups, Bruhat order, etc.

Check the bottom of the page for some pictures.

Getting started

Documentation

All functions are documented in the usual Macaulay 2 documentation style and come with examples. Thus, to view the documentation corresponding to the whole package, type help "WeylGroups" or viewHelp "WeylGroups" to open it in your web browser.

A quick tutorial is then accessible from that main documentation page or by opening the file tutorial.html coming with the package.

Here are some examples of Hasse diagrams obtained using this package, together with the package Graphics to produce svg output directly embeddable in a webpage.

The left diagram is the hasse diagram of the Bruhat order relation on the quotient of the Weyl group of a root system of type A4 modulo a parabolic subgroup of a root system of type A1. The right diagram is instead F4 modulo A1 times A2.