Abstract

Several very interesting results connecting the theory of abelian ideals of Borel subalgebras, some ideas of D. Peterson relating the previous theory to the combinatorics of afine Weyl groups, and the theory of discrete series are stated in a recent paper (Kostant, 1998) by B. Kostant.

In this paper we provide proofs for most of Kostant’s results extending them to ad-nilpotent ideals and develop one direction of Kostant’s investigation, the compatible discrete series.

Authors