In the early 2000s, Ranee Brylinski constructed (g,K)-modules with the property that their K-structure matches the structure of regular functions on classical nilpotent varieties. In this talk, we give a description on the composition factors of these modules. In particular, we completely decompose the ring of regular functions of these varieties into irreducible, algebraic modules. We will also mention its significance in studying the normality of these varieties, and its relations with the Orbit Method.

This is a joint work with Dan Barbasch.