Notes from the AIM
Read me first
The atlas projected hosted two workshops for graduate students and
postdocts, summer 2009 and summer 2013.
Some more detail on the mathematics
Representation theory of Real Groups
(Jeffrey Adams and Fokko du Cloux)|
|Fairly complete explanation of the
basic atlas algorithm, up to but not including the KLV
|Combinatorics for the Representation Theory of
Real Groups (Fokko du Cloux)|
|Notes by Fokko du Cloux on the atlas algorithm.
Somewhat out of date now (2005), but still useful for many fundamental
algorithms for structure theory.|
Equivalence of Parameters (Jeffrey Adams)|
||Detailed statement of the classification, including the precise notion of
equivalence of parameters. This is particularly subtle (and critical)
in the case of singular infinitesimal character. |
Representations of K (David Vogan)|
||Detailed description of the irreducible representations of
K in terms suitable for the Atlas.
Also see notes by Peter Trapa from Palo Alto, 2005
Discrete Series and Characters of the
Component Group (Jeffrey Adams)
Computing the signs which occur in endoscopic lifting of discrete
series representations, in the context of the atlas algorithm. These
are the "kappa" signs of Shelstad. Includes a self-contained
description of the algorithm in the case of discrete series.
Computing Hodge Filtrations
(Jeffrey Adams, Peter Trapa and David A. Vogan Jr.
Wilfried Schmid and Kari Vilonen have made a conjecture relating mixed Hodge
modules and the unitary dual of a real reductive group. This article is intended
to be progress in the direction of proving this conjecture. The main result is
that the canonical Hodge filtration on a Harish Chandra module, when reduced modulo 2,
gives the signature of the canonical c-form. This result would be a consequence
of the main conjecture of Schmid and Vilonen.
Miscellaneous auxiliary papers
Generalized Harish-Chandra modules
These papers of interest mostly to experts.