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Quivers, their representations and quiver varieties

Sergey Arkhipov
Eulers Venner
Torsdag, 20 september, 2012, at 16:15-17:00, in Aud. D1 (1531-113)
We review representation theory of quivers. Gabriel's theorem and Ringel's results of the 90's relate representations of A, D, E type quivers with quantum enveloping algebras of simple Lie algebras. We review this construction. Lusztig transferred the idea to pass directly from a Dynkin graph to the corresponding Lie algebra by means of representations of quivers to geometry. We introduce quiver varieties and discuss the relation of their geometry to the theory of crystal bases. We explain how categorification of quantum groups appears naturally in this context.
Kontaktperson: Benjamin Randeris Johannesen