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Sponsor: NSF, CONACyT
Homepage: http://msri.org/activities/events/9900/qgroups/
Email: qgroups@msri.org
Organizers: Susan Montgomery (USC), Jose Antonio de la Pena (UNAM), Claudio Procesi (U. of Roma), Nicolai Reshetikhin (UCB)
Description:
Quantum groups emerged from mathematical physics in mid 80's as an algebraic structure hidden behind quantum
integrable systems. Algebraically quantum groups are Hopf algebras which are noncommutative deformations of
functions on Lie groups, or dualizing, non-commutative deformations of universal enveloping algebras of Lie algebras.
Immediately after these structures were discovered they were used to construct new invariants of knots and 3-manifolds.
One of the most important discoveries in representation theory in the 90's was the universal (crystal) basis discovered by Kashiwara and Lusztig, discovered using quantum groups, and more recently, Nakagima and others constructed representations of affine Lie algebras and corresponding quantum groups using geometry of certain moduli spaces. Another area where quantum groups clarified a lot the existing results and made possible fast progress in the theory of special functions (q-special functions). Conceptually, this direction can be regarded as harmonic analysis on quantum groups. Yet another direction emerged from study of the study of Hopf algebras with real structure by means of functional analysis. This direction, is well represented in the community of people working in C*-algebras.
Topics to be covered in the conference are as follows:
Finite dimensional Hopf algebras Geometric realizations of quantized universal enveloping algebras Applications of quantum groups Representation theory of quantum groups
Mail Address:
Quantum Groups Mathematical Sciences Research Institute 1000 Centennial Drive Berkeley, CA 94720-5070.
Date received: August 27, 1999
© 2008 Atlas Conferences Inc.