# Combinatorics of Harish-Chandra modules

These lectures (given at a NATO-workshop 1997 in Montreal) survey recent work on the combinatorics of
certain infinite dimensional representations of complex semisimple Lie
algebras. Their focus is not on understanding the irreducible objects but
rather on understanding the structure of suitable representation categories.
They concentrate on the relation of these representation categories
with categories of modules over the
coinvariant algebra associated to the action of the Weyl group
on a Cartan subalgebra. We also discuss conjectural generalizations
to the representation theory of real Lie groups.