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 seminar has concluded for now. Thank you for your attendance!
We are going to continue, based on demand, with an Atlas Help Session.
We will answer any and all questions (that we can...) about the software and the mathematics behind it.
Please send an email to Jeff Adams (jda@math.umd.edu) if you would like to discuss anything this week.
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 reverse chronological order)
Date | Speaker | Title | Video | Slides |
February 2 |
Jeffrey Adams |
Some examples
| video
|
|
January 26 |
David Vogan |
Computing Unitary Duals III: unitary_dual@RealForm
| video
|
slides
|
January 19 |
David Vogan |
Computing Unitary Duals II: non-unitary certificates
| video
|
slides
|
January 12 |
David Vogan |
Computing Unitary Duals I: cohomological induction
| video
|
slides
|
December 15 |
Adams/Vogan |
Interesting examples of Arthur packets, computed by Annegret's script
| video
|
slides
|
December 8 |
David Vogan |
More on honest Arthur packets/Annegret Paul's magic scripts
| video
|
slides
|
December 1 |
David Vogan |
More on honest Arthur packets/Annegret Paul's magic scripts
| video
|
slides
|
November 17 |
Jeffrey Adams/David Vogan |
Arthur Packets for G2/Induction for Arthur packets |
video
|
slides
|
November 10 |
Jeffrey Adams |
Arthur Packets for G2 |
video
|
slides
|
November 3 |
Jeffrey Adams |
Examples of Duality/Miscellaneous 2
| video
|
slides
|
October 27 |
Jeffrey Adams |
Examples of Duality/Miscellaneous
| video
|
slides
|
October 20 |
David Vogan |
Duality, associated varieties, and nilpotent orbits 3
| video
|
slides
|
October 13 |
David Vogan |
Duality, associated varieties, and nilpotent orbits 2
| video
|
slides
|
September 29 |
David Vogan |
Duality, associated varieties, and nilpotent orbits
| video
|
slides
|
September 22 |
Jeffrey Adams |
Cohomological Arthur packets 3
| video
|
slides
|
September 15 |
Jeffrey Adams |
Cohomological Arthur packets 2
| video
|
slides
|
September 8 |
Jeffrey Adams |
Cohomological Arthur packets
| video
|
slides
|
September 1 |
David Vogan |
More about discrete series restriction
| video
|
slides
|
August 25 |
David Vogan |
Cohomological induction and restricting discrete series to K | video
|
slides
|
August 18 |
Jeffrey Adams |
Hermitian forms on finite dimensional representations | video
|
slides
|
August 11 |
David Vogan |
More on duality for singular and non-integral infinitesimal character | video
|
slides
|
August 4 |
David Vogan |
Duality for singular and non-integral infinitesimal character
| video
|
slides
|
July 28 |
Jeffrey Adams |
Vogan duality and Arthur Packets
| video
|
slides
|
July 21 |
Jeffrey Adams |
Vogan duality
| video
|
slides
|
July 7 |
David Vogan |
Affine Weyl group, facets, and the unitary dual
| video
|
slides
|
June 30 |
David Vogan |
Classifying the unitary dual (part 1 of infinitely many...)
| video
|
slides
|
June 23 |
David Vogan |
Dirac Operator in Atlas
| video
|
slides
|
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.
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