ON THE ASSOCIATED CYCLES OF DISCRETE-SERIES REPRESENTATIONS

Let (G, K) be a classical symmetric pair defined by the involution a o n G. Let (g, f) be the corresponding Lie algebras. Given a theta-stabl e Borel subalgebra b we determine a dense K-orbit in K.(b (perpendicul ar to) boolean AND i (perpendicular to)). In the case when (G, K) is o f type AIII or BDI, we use this information to compute the harmonic po lynomial determined by the associated cycle of a large discrete series representation. (C) 1998 Academic Press.