Atlas of Lie Groups and Representations

Archived web site of the Workshop on the Atlas of Lie Groups and Representations, Salt Lake City, July 10–21, 2017. This is an archived copy, kept as it was; dates, registration, travel and contact details are those of the event. All Atlas workshops

Workshop on Unitary Representations of Real Reductive Groups

See Slides, videos, and IO for videos of every lecture, as well as slides and computer input/output of some of them.

Schedule Week 1

Monday, July 10
9-10:15: David Vogan I: Overview
10:30-11:45: Jeffrey Adams I: The Atlas point of view
1:30-2:45: Marc van Leeuwen I: Introduction to the Atlas programming language
3:15-4:30: Interactive session
7:30-9 PM: Evening help session

Tuesday, July 11
9-10:15: David Vogan II: Langlands classification part 1 (see notes from Vogan I)
10:30-11:45: Jeffrey Adams II: More on the Atlas point of view
1:30-2:45: Marc van Leeuwen II: Introduction to the Atlas programming language 2
3:15-4:30: Interactive Session
7:30-9 PM: Evening help session

Wednesday, July 12
9-10:15: David Vogan III: Langlands classification part 2
(see notes from Vogan I) 10:30-11:45: Jeffrey Adams III: Atlas point of view 3 (parameter in atlas)
1:30-2:45: Annegret Paul I: Parabolic subgroups, real Parabolic induction
3:15-4:30: Interactive Session
7:30-9 PM: Evening help session

Thursday, July 13
9-10:15: David Vogan IV: Hermitian forms
10:30-11:45: Peter Trapa I: Cohomological induction
1:30-2:45: Marc van Leeuwen III: Introduction to the Atlas programming language 3
3:15-4:30: Interactive Session
7:30-9 PM: Evening help session

Friday, July 14
9-10:15 David Vogan V: c-form, computing c and Hermitian forms
10:30-11:45 Adams IV: Character formulas and composition series
1:30-2:45: Annegret Paul II: Cohomological induction in Atlas
3-4:30: Interactive Session

Schedule Week 2

The details of the schedule the second week will depend to some extent on the first week and input from attendees.

Monday, July 17
9-10:15: David Vogan VI: computing Hermitian form (see first lecture for slides)
10:30-11:45: Annegret Paul: K-types in Atlas
1:30-2:45: Example of K-types: some representations of Spin(4,4) and Spin(5,3)
3:15-4:30: TBA
7:30-9 PM: Evening help session

Tuesday, July 18
9-10:15: David Vogan: geometry of the twisted setting
10:30-11:45: Jeffrey Adams: twisted KLV polynomials
1:30-2:45: Paul Mezo: Atlas and twisted endoscopy for GL(n,R)
3:15-4:30: TBA
7:30-9 PM: Evening help session

Wednesday, July 19
9-10:15: Peter Trapa: Cells and associated varieties
10:30-11:45: TBA
1:30-2:45: Jonathan Fernandes: unipotent Arthur packets in Atlas
3:15-4:30: Roger Zierau: annihlators of Harish-Chandra modules
7:30-9 PM: Evening help session

Thursday, July 20
9-10:15: Vogan Duality
10:30-11:45: Coherent Continuation
1:30-2:45: deformation of representations
3:15-4:30:
6:00 Banquet at Indochine Vietnamese Bistro, 230 S 1300 E

Friday, July 21
9-10:15 Jeffrey Adams: complex groups in atlas
10:30-11:45 David Vogan: twisted representations of Weyl groups
The workshop will end around noon on Friday.

Possible topics include:

  • Structure theory: constructing groups in different ways, the component group, the center, Galois cohomology
  • Parabolics: complex, real, and theta-stable parabolics and Levi factors
  • Real and cohomological induction, including techniques for studying cohomological induction outside the usual range
  • Composition series and character formulas
  • Computing c-invariant and Hermitian forms
  • Working with Kazhdan-Lusztig-Vogan polynomials
  • Computing the Jantzen filtration
  • Translation functors and coherent continuation
  • Computing with cells
  • Maximal compact subgroup: understanding K and its representations
  • Lowest K-types and branching to K
  • Signatures of finite dimensional representations
  • Computing the Weyl character formula
  • Nilpotent orbits and unipotent representations

Supported by NSF grant DMS-0968275 and the University of Utah