CORDIS Project
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This project investigates the unitary dual of locally compact groups by analyzing generalized principal series linked to Poisson boundaries from random walks. The aim is to uncover irreducible representations and their relationships through the study of ergodic properties and character formulas.
Locally compact groups have many unitary representations.
For example, the regular representation, or more generally, the quasi-regular representations arising as function spaces over group actions.
These representations can be written as direct integrals of irreducible ones.
The space of all irreducible unitary representations is the ""unitary dual"" of the group.
It exists, and has a Borel structure and a funny topology that can be described abstractly, but the truth is, that for a general gro…
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