17/07/2013, 15:00 — 16:00 — Room P3.10, Mathematics Building Peter Trapa, University of Utah
Unitary representations of reductive Lie groups
Unitary representations of Lie groups appear in many parts of
mathematics: in harmonic analysis (as generalizations of the sines
and cosines appearing in classical Fourier analysis); in number
theory (as spaces of modular and automorphic forms); in quantum
mechanics (as "quantizations" of classical mechanical systems); and
in many other places. They have been the subject of intense study
for decades, but their classification has only recently recently
emerged. Perhaps surprisingly, the classification has inspired
connections with interesting geometric objects (equivariant mixed
Hodge modules on flag varieties). These connections have made it
possible to extend the classification scheme to other related
settings. The purpose of this talk is to explain a little bit about
the history and motivation behind the study of unitary
representations and offer a few hints about the algebraic and
geometric ideas which enter into their study. This is based on a
recent preprint with Adams, van Leeuwen, and Vogan.
