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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