Notes from the AIM workshops

Miscellaneous Notes

Computing Twisted KLV Polynomials, by Jeffrey Adams. The main goal is explicit recursion relations for the "twisted" KLV polynomials studied by Lusztig and Vogan. (Updated 4/12/13).

Infinite Dimensional Representations of Real Reductive Groups, by David Vogan, from the Utah Workshop, 2012. Also see the slides from the Utah workshop

Algorithms for Representation theory of Real Groups by Jeffrey Adams and Fokko du Cloux [updated 7/18/08]

Computing Global Characters (revised 4/20/2011) by Jeffrey Adams

On the Structure of the Fundamental Series of Generalized Harish-Chandra Modules by Ivan Penkov and Gregg Zuckerman

Improved Recursion Formulas for KLV Polynomials (Adams/Trapa/Vogan): includes some new relations which simplify the computation

Computing the Kazhdan-Lusztig Algorithm, informal notes by Fokko du Cloux, on computational aspects of the KLV polynomials; revised summer 2011 to incorporate new recursion relations from Improved Recursion Formulas for KLV Polynomials

Representations of K - by David Vogan (updated 3/27/06) - detailed description of the irreducible representations of K in terms suitable for the Atlas. Also see notes by Peter Trapa from Palo Alto, 2005

Generalized Harish-Chandra Modules by Gregg Zuckerman

The Contragredient (Vogan/Adams, updated 1/2/12).

Unitary Genuine Principal Series of the Metaplectic Group by Alessandra Pantano, Annegret Paul and Susana Salamanca-Riba
Notes on the Hermitian Dual preliminary notes by Jeffrey Adams
Notes on Doubly Extended Groups - preliminary notes for the cognoscenti [updated 3/8/09]
Computing Unipotent Representations Using the Atlas Software (slides from talk at Kalamazoo, 10/19/2008) by Jeffrey Adams

Assigning Representation Parameters to Atlas Block Output by Annegret Paul. How to convert the output of the block command into something that is understandable by a human.

Hermitian forms for Sp(4,R) (Jeffrey Adams and Annegret Paul), notes on computing Hermitian forms in an example, for the experts. Update 4/8/12.

Implementation of the Kazhdan-Lusztig algorithm (pdf version). These are technical notes about computing Kazhdan-Lusztig-Vogan polynomials for real groups. They were written by Fokko du Cloux for his own use.

Guide to the Atlas Software: Computational Representation Theory of Real Reductive Groups by Jeffrey Adams (dvi file). (Former title: Examples of the Atlas Software)

Discrete Series and Characters of the Component Group by Jeffrey Adams
A note on Kazhdan-Lusztig conjecture and signature of invariant Hermitian forms (notes by Fokko du Cloux)

Some Notes on Parametrizing Representations by Jeffrey adams (dvi) - these are some technical notes, for the experts
Computing y (pdf file) - for the cogno-cognoscenti

Strong real forms and the Kac classification by Jeffrey Adams (dvi) an expository treatment of the Kac classification of real forms

Computing the Unitary Dual by David A. Vogan Jr.

A Langlands Classification for Unitary Representations by David A. Vogan Jr., from Advanced Studies in Pure Mathematics, Volume 26 (1998), pp. 1-16

Lecture by Jeffrey Adams at Rutgers, March 7, 2003

Minicourse by J. Adams at the University of Maryland, October 2002:

   Lecture I: Finite groups and SL(2,R)

   Lecture II: Root systems and Weyl groups

   Lecture III: Unitary Representations of real Lie groups, with an appendix on mathematical software

Powerpoint slides of lecture by J. Adams, Singapore, August 2002

Notes from lectures by by David A. Vogan Jr., Montreal, June 2002

Notes for lectures at Snowbird, June 4-8, 2006; and the slides from the lectures.

Talk by Jeffrey Adams at the Washington/Baltimore meeting of SIAM, November 2004