As a postdoc at UGA, I became involved in the VIGRE Algebra research group. This is a large research group including graduate students, postdocs, and senior faculty, working for several years on projects in representation theory of algebraic groups. The focus is on Lie algebra cohomology, and thus there are a number of connections with tools from algebraic topology. Moreover, there are parts of the work that can be reduced to finite (but non-trivial) Weyl group calculations, and thus to computer programs—one does not need to have a strong background in algebraic groups for this aspect of the project.

Composition factors of Weyl modules ¶

Adamovich and Kleshchev-Sheth give combinatorial algorithms for determining the composition factors of certain algebraic groups and the symmetric groups. As part of the project on low-degree cohomology, we developed Sage code to implement these algorithms and draw the resulting posets of composition factors.

If you're interested in using it, the source code is completely documented (over 400 doctests) and available under the GPL. And if you have further questions or comments, I would love to hear from you! To use the code, just download the .py Sage source file, and load it into your Sage session. The .patch file is an alternative format; just ignore it if you don't know what it is.

• Sage source: kleshchev_sheth.py
  (after download, change file ending from _py.txt to .py)
• A Sage patch: kleshchev_sheth.patch
  (adds source code and documentation to your Sage install)
• Complete HTML documentation

tags: rep-thy | software