Atlas of Lie Groups and Representations

Seminar Series 2022

Real Reductive Groups/Atlas of Lie Groups and Representations Seminar

The seminar is running on Zoom, on Thursdays, 10:30 AM - noon (EST), starting on Thursday January 6.

The home page for the seminar is on the Research Seminars web site: Research Seminars/Atlas See below for an overview.

There you'll find an introduction to the seminar, suggested background reading, the Zoom link and a schedule of talks.

The talks are being recorded. The recordings and slides will made available here and at Research Seminars/Atlas.

There is a Slack Worskspace for discussing the software. Click on this link to join. Use this workspace for questions and discussions about all aspects of the A tlas software.

There will be a Zoom help session on installing the atlas software, Wednesday January 5, 9:00 to 11:00 EST. The password is 5 characters, the first two (capital letter, number) are the name of the largest exceptional group, and the next three its dimension. This is the same link/password where the seminar lectures will be.

Links to completed lectures and slides.

The links to the individual talks in the table below may (or may not?) require you to be logged in to a Microsoft account. If that's an issue use this link to the entire Notebook of all the slides; you can access the slides for the individual talks from there.

Jan 6 David Vogan What Groups/Representations/Software? video slides
Jan 13 Jeffrey Adams Root Data/Complex and Real reductive groups video slides
Jan 20 David Vogan Parameter for Representations video slides

Beginning January 6, 2022.

This is will be 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. We'll use the atlas software; you should follow the directions at to install it on your laptop.

The aim is for each seminar to last approximately one hour; the extra half hour in the schedule is 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.

A good general introduction to what the seminar is about can be found at

from a 2017 workshop. The mathematical subject matter is described in slides

from Vogan's lecture. The main ideas about how to realize this mathematics on a computer are described in Adams's lecture

A quick introduction to the syntax for the software is in van Leeuwen's presentation

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.