Unipotent Representations Attached to the Principal Nilpotent Orbit

Abstract

In this paper, we construct and classify the (special) unipotent representations of a real reductive group attached to the principal nilpotent orbit. Our construction gives rise to a formula for the K-types and associated varieties of all such representations.

Upper Triangularity for Unipotent Representations

“…This result is strong evidence in favor of the strategy outlined above: the unipotent representations attached to non-induced orbits are indeed the building blocks from which all others can be formed. There is some hope that the relationship between Unip(O l ) and Unip(O g ) can be made extremely precise in certain special cases (in [15], this is achieved for the principal nilpotent orbit).…”