Mathematics Colloquium, Spring 2004
Special Lecture presented by

Hall algebras, quiver varieties, and generalized Schur-Weyl duality

One of the oldest concepts of the geometric representation theory is that of Hall algebras. The idea is to use the set (or the variety) of Jordan-Holder filtrations of modules of an associative algebra A to construct the algebra of characters (or a category of representations) of an algebraic group G. I will explain the original Hall theory (A=k[[x]], G=GL) and its recent generalizations including the approach via quiver varieties.

I will indicate my motivations for this work which include the instanton moduli space and the local Langlands correspondence, but most of the talk will be elementary.

Tuesday, January 20, 2004, 445 Altgeld Hall, 2:00 p.m.