Informal Friday Seminar: Romanov -- The Lusztig-Vogan module of the Hecke algebra

This talk will be a continuation of last week’s IFS talk on the Lusztig-Vogan module of
the Hecke algebra. More details can be found below. 

Let G be a real reductive Lie group (think GL(n,R)).  When studying the representation
theory of such a group, one quickly encounters a well-behaved class of representations
called admissible representations.  The combinatorial behaviour of these representations
(e.g.  composition series multiplicities of standard representations) is captured
by a certain geometrically-defined module over the associated Hecke algebra, the
Lusztig-Vogan module.  In this talk, I will describe the construction of the
Lusztig-Vogan module, then we will see what it looks like explicitly in some SL2
examples. If we are lucky, we might get a glimpse of a mysterious feature called Vogan
duality.