Structure of tempered homogeneous spaces - Part 1/3: Dynamical approach
Appears in collection : 2025 - T1 - Representation theory and noncommutative geometry
The three lectures introduce recent theories of tempered spaces, and I plan to provide an overview of these topics, using plenty of elementary examples to make the basic concepts and key ideas more accessible.
In the first lecture, I will review basic concepts such as tempered unitary representations of real reductive groups, like $GL(n, R)$, as well as “tempered spaces” and “tempered subgroups”. I will begin with some geometric observations of group actions, including the properness criterion for reductive homogeneous spaces. Subsequently, I will introduce a “quantification” of proper actions and incorporate a dynamical approach into analytic representation theory, including the temperedness criterion for homogeneous spaces, which was developed recently by Y. Benoist and the speaker, drawing on the Cowling-Haagerup-Howe theory and other related ideas.
