On the Associated Cycles of Discrete Series Representations

Let (G, K) be a classical symmetric pair defined by the involution θ onG. Let ( , ) be the corresponding Lie algebras. Given a θ-stable Borel subalgebra we determine a denseK-orbit inK • ( ∩ ). In the case when (G, K) is of type AIII or BDI, we use this information to compute the harmonic polynomial determined by the associated cycle of a large discrete series representation.