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This research delves into the representation theory of topological groups, particularly focusing on harmonic analysis related to reductive groups over local fields. It aims to develop tools for analyzing invariant distributions and advance understanding in the theory of automorphic forms.
One can view the representation theory of a topological group as non-commutative harmonic analysis on the group.
For compact groups this view is justified by the Peter-Weyl theorem.
The relative representation theory of a group is harmonic analyses on spaces with transitive group action.I work in relative representation theory of reductive (algebraic) groups over local fields, e.g. the general linear group over the field of real numbers or the field of p-adic numbers.
This theory has applicati…
WEIZMANN INSTITUTE OF SCIENCE
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