In joint work with Tymoczko, we define a set of exponents for each upper
order ideal in the poset of positive roots. This generalizes the usual
notion of exponents (which we recover when the ideal is the empty set).

The talk deals with two conjectures for these exponents which generalize
classic theorems: one concerns a factorization of an analogue of the
Poincare polynomial of the Weyl group; the other concerns a factorization
of the characteristic polynomial of an associated hyperplane arrangement.
We explain a proof of these conjectures in types A, B, and C.

(joint talk with Lie Groups Seminar)