Seminário de Álgebra  RSS

17/07/2013, 15:00 — 16:00 — Sala P3.10, Pavilhão de Matemática
, 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.

Organizador actual: Gustavo Granja

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