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.

We are taking a one week break: there is no seminar on Thursday June 16. We'll be back the following week (June 23) at the usual time.

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.

Schedule and links to previous talks (in revere chronological order)

DateSpeakerTitleVideoSlides
June 9 Jeffrey Adams Loose ends, Jantzen filtration, Questions from the audience video slides
June 2 Jeffrey Adams Loose ends: More on translation, some answers to questions video slides
May 26 Jeffrey Adams Loose ends: Hermitian representations, translation, the Jantzen filtration video slides
May 19 David Vogan Unitary Dual of F4_B4 in atlas video slides
May 12 David Vogan Unitary Dual of SO(2n,1) in atlas video slides
May 5 Jeffrey Adams Theta-stable parabolic subgroups and cohomological induction in atlas video slides
April 28 David Vogan Real parabolic subgroups and induction in atlas video slides
April 21 Jeffrey Adams Unipotent Representations, Nilpotent Orbits and the Weyl group II video slides
April 14 Jeffrey Adams Unipotent Representations, Nilpotent Orbits and the Weyl group I video slides
April 7 David Vogan Nilpotent orbits and atlas video slides
March 31 David Vogan Gelfand-Kirillov dimension and atlas video slides
March 24 Jeffrey Adams Weyl group representations in Atlas II video slides
March 17 Jeffrey Adams Weyl group representations in Atlas I video slides
March 10 David Vogan How atlas does what it says its doing video slides
March 3 Jeffrey Adams Signature character formulas and unitary representations 2 (Here is the SL2 refcard from the talk) video slides
Feb 24 Jeffrey Adams Signature character formulas and unitary representations (or why we needed this software in the first place) video slides
Feb 17 David Vogan Character formulas and Kazhdan-Lusztig polynomials (or why we needed this software in the first place) video slides
Feb 10 Jeffrey Adams The Atlas Way (More on KGB) video slides
Feb 3 David Vogan Understanding K: How Atlas understands compact subgroups video slides
Jan 27 Jeffrey Adams Branching to K video slides
Jan 20 David Vogan Parameters for Representations video slides
Jan 13 Jeffrey Adams Root Data/Complex and Real reductive groups video slides
Jan 6 David Vogan What Groups/Representations/Software? 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 http://www.liegroups.org/ 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

www.liegroups.org/workshop2017/workshop/videos_and_computer

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

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.