Speaker: Jeffrey Adams, University of Maryland
The Atlas of Lie Groups and Representations
One of the fundamental problems in the theory of Lie groups
is to classify the Unitary Dual of a group G: the irreducible
representations of G, acting on a (typically infinite dimensional)
Hilbert space, preserving the inner product. This is a very difficult
problem, unsolved except in some special cases, and the answer is
known to be very complicated.
The primary goal of the Atlas project is to compute the Unitary Dual by computer, even though it is not obvious there is a finite algorithm in principle, not to mention in practice. An important auxiliary goal is to provide software for doing computations in Lie theory and representation theory.
I'll discuss the current state of the project, in broad terms, and talk about what we've learned by rethinking our entire subject in computational terms.
Department of Mathematical Sciences
George Mason University
4400 University Drive, MS 3F2
Fairfax, VA 22030-4444
Tel. 703-993-1460, Fax. 703-993-1491