Speaker: David Vogan (MIT)
Title: Extended reductive groups and representation theory
Location: Room C415A at the CUNY Graduate Center (365 Fifth Avenue, Manhattan)
Time: Friday, April 19, 2013 from 2:00 to 3:00 pm
Abstract: Suppose G is a complex connected reductive algebraic group, and \Sigma is a finite group. An "extended group" is an extension of \Sigma by G; that is, a group having G as a normal subgroup, with quotient \Sigma. One of the most important examples of such extended groups is Langlands's L-group, which is an extension of a Galois group by a reductive group.
I will discuss several ways in which extended groups arise in parametrizing rational forms and representations of reductive groups. Then I'll discuss some problems arising in recent joint work with Lusztig about the representation theory of extended groups themselves.