Real Reductive Groups/Atlas of Lie Groups and Representations Seminar

This was a working/learning seminar on (infinite-dimensional) representations of real reductive groups, aimed at grad students and researchers having some familiarity with representations of compact Lie groups. It used the atlas software; participants installed it on their laptops following the directions on the software page.

The aim was for each seminar to last approximately one hour; the extra half hour in the schedule was meant to encourage lots of interaction with the audience. The idea of the seminar is that learning how the software does mathematical computations is an excellent way to understand the mathematics, as well as a great source of examples.

First goal is to learn how the software represents real reductive groups (precisely, the group of real points of any complex connected reductive algebraic group) and their representations; making sense of the software will lead to an understanding of the underlying mathematics. Second goal is to use the software to investigate experimentally questions about reductive groups.

A good general introduction to what the seminar is about can be found at www.liegroups.org/workshop2017/workshop/videos_and_computer from a 2017 workshop. The mathematical subject matter is described in the slides www.liegroups.org/workshop2017/workshop/presentations/voganHO.pdf from Vogan’s lecture. The main ideas about how to realize this mathematics on a computer are described in Adams’s lecture www.liegroups.org/workshop2017/workshop/presentations/adams1HO.pdf. A quick introduction to the syntax for the software is in van Leeuwen’s presentation www.liegroups.org/workshop2017/workshop/computer_transcripts/vanLeeuwen1.out.

The home page for the seminar is on the Research Seminars web site: Research Seminars/Atlas. There you’ll find an introduction to the seminar, suggested background reading and a schedule of talks.

When the seminar concluded, it was to continue, based on demand, as an Atlas Help Session, answering questions about the software and the mathematics behind it. There is a Slack workspace for questions and discussions about all aspects of the atlas software: join the workspace.

Talks are listed in reverse chronological order. The recordings are on MIT Zoom. The links to the slides for individual talks may require you to be logged in to a Microsoft account; if that’s an issue, use the notebook of all the slides and open the slides for individual talks from there.