  Let G be a simple algebraic group over the complex numbers containing a Borel
subgroup B. Given a B-stable ideal I in the nilradical of the Lie algebra of B,
we define natural numbers $m_1, m_2, ..., m_k$ which we call ideal exponents.
We then propose two conjectures where these exponents arise, proving these
conjectures in types A_n, B_n, C_n and some other types.
  When I is zero, we recover the usual exponents of G by Kostant and one of our
conjectures reduces to a well-known factorization of the Poincare polynomial of
the Weyl group. The other conjecture reduces to a well-known result of
Arnold-Brieskorn on the factorization of the characteristic polynomial of the
corresponding Coxeter hyperplane arrangement.
