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Atlas of Lie Groups and Representations | |||
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The Atlas of Lie Groups and
Representations is a project to make available information about
representations of reductive Lie groups over real and p-adic fields.
Of particular importance is the problem of the unitary dual:
classifying all of the irreducible unitary representations of a given Lie group.
The Atlas consists in part of a project to compute the
unitary dual, by mathematical and computational methods.
We are also planning to make information about Lie groups and
representation theory, in particular unitary representations,
available to the general mathematical public.
You may have heard about our computation
Kazhdan-Lusztig polynomials for the split real group E8.
Here are some details of the
calculation, and David Vogan has written a narrative of the project.
There is an introduction to the calculation at
AIM.
For more information on the E8 calculation there are
some slides of talks available in the talks section.
Also see David Vogan's
home page,
and here are some more technical details on
what we really did.
The atlas software runs under unix, and is
freely available from the software page.
Here are the main parts of the Atlas web site:
Web interface to the
atlas software.
Papers:
Expository notes, notes of lectures, etc.
Talks:
Slides from various public lectures,
including David Vogan's lecture announcing the E8 calculation, March 19, 2007
Workshop and conference web sites.
Spherical Unitary Explorer:
an interactive tool for learning about spherical unitary
representations of classical groups
Tables:
Tables computed using the Atlas and associated software.
Includes:
Atlas wiki:
public wiki for discussion of the atlas project
People who are working on the Atlas project.
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