Notes from the AIM workshop, Palo Alto, July 2008 (schedule of talks)

• John Stembridge: More W-Graphs and Cells: Molecular Components and Cell Synthesis
• Annegret Paul: Assigning Representation Parameters to Atlas Block Output
• David Vogan: Affine Weyl group and coherent families (notes by Siddhartha Sahi)

Notes from the workshop at Maryland, March 15-18, 2008

• John Stembridge: Admissible W-Graphs (slides for John's talk at MSRI)
• Alfred Noel and Stephen Jackson: Nilpotent Orbits Associted to Coxeter Cells
• David Vogan: Honest Arthur Packets (notes by Annegret Paul)
• David Vogan: Real Reductive Subgroups of Equal Rank (notes by Tatiana Howard)
• Birne Binegar: Tau Signatures, Cells and Orbits
• Jeffrey Adams: Stability (notes by Dan Ciubotaru)
• David Vogan: Generalized Induction (notes by Siddhartha Sahi)
• Peter Trapa: Parametrizing Real Even Nilpotent Coadjoint Orbits using Atlas

Notes from the AIM workshop, Palo Alto, July 2007 (schedule of talks)

• Jeffrey Adams: Computing Global Characters Using Atlas
• Birne Binegar: A fine partitioning of cells
• Peter Trapa: Cells (notes by Peter Trapa and Patrick Polo)
• David Vogan: More Cells (notes by Patrick Polo)
• Monty McGovern: Nilpotent Orbits (notes by Patrick Polo)
• David Vogan: Associated Varieties (notes by Patrick Polo)
• John Stembridge: Synthetic W-Graphs and cells
• Annegret Paul: How to attach a representation to a pair (x,y)
• Peter Trapa and Dan Ciubotaru: Functors for Matching Kazhdan-Lusztig polynomials for GL(n,R) (slides from talk)
• Alfred Noel: Bala-Carter type classification of nilpotent orbits of real Lie groups

• Birne Binegar: On a Family of Nilpotent K(C) orbits
• Dan Ciubotaru and Peter Trapa:Composition Factors for the Graded Hecke Algebra
• Scott Crofts: Algorithms for Representation Theory
• Alessandra Pantano: Multiplicities of K-types in Principal Series
• Susana Salamanca and Annegret Paul: On the omega-regular unitary representations of Mp(2n,R)
• David Vogan: Some observations about Kazhdan-Lusztig Polynomials
• Wai-Ling Yee:Signatures of Invariant Hermitian Forms on Irreducible Highest Weight Modules and Signed Kazhdan-Lusztig Polynomials
• Alfred Noel: Software for computing standard representations

• Scott Crofts: Closure Relations of K-orbits on G/B
• Peter Trapa: Computing Real Weyl Groups
• John Stembridge: A Practical View of W^{^}
• John Stembridge: A bried demonstration how to use the Coxeter package to do calculations with W^{^} (text file)
• Jeffrey Adams: Software Project: Weakly Fair A_q(lambda) (dvi file)
• Peter Trapa: On the Computations of Characteristic Cycles of Harish-Chandra Modules (dvi)
• Annegret Paul: Representations with Non-integral infinitesimal character
• Alessandra Pantano: On the double cover of split F and its petite K-types
• David Vogan (notes by Alfred Noel): Parametrizing representations of K
• Dan Ciubotaru: On the Unitary Dual of Hecke Algebras with Unequal Parameters (also Dan's notes from Snowbird on Spherical Unitary Representations for Split Groups
• Jeffrey Adams: User Guide to the Atlas Software (very early version)
• Jeffrey Adams: Specifications for Version 1.0 of the software [updated 3/16/07] pdf version
• Dan Barbasch (notes by Dan Ciubotaru): Cells in Weyl Groups and Primitive Ideals
• Wai Ling Yee: Signatures and Cohomological Induction

• Siddhartha Sahi: Graded K-multiplicities
• Jeffrey Adams: Parameters for Real Groups (revised from last year)
• Jeffrey Adams: Real Forms and Strong Real Forms: Quick Reference Guide
• Fokko du Cloux: Combinatorics for the representation theory of real reductive groups - (postscript version)
• Peter Trapa: Computing K-type multiplicites in standard representations (after Vogan)[updated 8/22/05]
• Alessandra Pantano: Unitarity of non-spherical principal series
• Alessandra Pantano: Petite and Relevant K-types for exceptional groups (slides): Introduction (slides) and list of K-types
• See Alessandra Pantano's notes on the unitary dual of split real groups from last year and Susana Salamanca's notes for David's talks (below).
• John Stembridge: Computing Discrete Series Multiplicities in the Connected Case (the Blattner formula)
• Wai Ling Yee: Signatures of Invariant Hermitian Forms on Highest Weight Modulesw

• Jeffrey Adams: Parameters for Real Groups (preliminary version)
• Dan Barbasch: Background on the Spherical Unitary Dual
• Fokko du Cloux: Algorithms for Structure Theory
• Alessandra Pantano: Weyl group representations and signatures of intertwining operators
• John Stembridge: Applying unitarity tests in the Weyl group
• John Stembridge: Non-Cellularity of Signatures ?

• David Vogan (notes by Peter Trapa): A Parametrization of K-Types
• David Vogan (notes by Alessandra Pantano): Notes on the unitary dual of real split groups
• David Vogan (notes by Susana Salamanca): Overview

Notes from the AIM workshop, Palo Alto, Summer 2003

• Dan Ciubotaru: Unitary Dual for P-Adic Groups of Type F₄
• John Stembridge: Lecture Notes for AIM/Atlas of Lie Groups Workshop
• Fokko du Cloux: Computing Kazhdan-Lusztig polynomials for real Lie groups
• Jiu-Kang Yu: Generic unitary spherical parameters
• David A. Vogan, Jr.: Branching Laws
• Siddhartha Sahi: The Step Algebra

Miscellaneous Notes:

Unitary Genuine Principal Series of the Metaplectic Group by Alessandra Pantano, Annegret Paul and Susana Salamanca-Riba
Notes on the Hermitian Dual (dvi file) - preliminary notes by Jeffrey Adams
Notes on Doubly Extended Groups (dvi) - 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
Algorithms for Representation theory of Real Groups by Jeffrey Adams and Fokko du Cloux [updated 7/18/08] (This was originally listed under the Summer 2006 talks). Here is a dvi file.

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.

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