Upper triangularity for unipotent representations
Suppose G is a real reductive group. The determination of the irreducible unitary representations of G is one of the major unsolved problem in representation theory. There is evidence to suggest that every irreducible unitary representation of G can be constructed through a sequence of well-understo...
| Main Author: | |
|---|---|
| Format: | Working paper |
| Language: | English |
| Published: |
ArXiv
2021
|
| Summary: | Suppose G is a real reductive group. The determination of the irreducible unitary representations of G is one of the major unsolved problem in representation theory. There is evidence to suggest that every irreducible unitary representation of G can be constructed through a sequence of well-understood operations from a finite set of building blocks, called the unipotent representations. These representations are `attached' (in a certain mysterious sense) to the nilpotent orbits of G on the dual space of its Lie algebra. Inside this finite set is a still smaller set, consisting of the unipotent representations attached to non-induced nilpotent orbits. In this paper, we prove that in many cases this smaller set generates (through a suitable kind of induction) all unipotent representations. |
|---|