MIT Combinatorics Seminar

Exponents for ideals of positive roots

Eric Sommers  (UMass Amherst)

Wednesday, October 27, 2004    4:15 pm    Room 2-338


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)