Covariant Projective Representations of Hilbert-Lie Groups
Erwin Schrödinger International Institute for Mathematics and Physics (ESI) via YouTube
Overview
Explore advanced mathematical concepts in this 54-minute lecture from the Thematic Programme on "Infinite-dimensional Geometry: Theory and Applications" at the Erwin Schrödinger International Institute. Delve into the theory of Hilbert-Lie groups, focusing on their representations and particularly examining the group U_2(H) of unitary Hilbert-Schmidt perturbations of the identity. Learn how covariance with respect to one-parameter group automorphisms implements regularity, and discover perturbation theory based on half-Lie groups that simplifies the study of compatible weight decompositions. Examine projective representations covariant for one-parameter group automorphisms, understanding how bounded extremal weights generate important representation families, and investigate how their central extensions and covariant extensions can be explicitly determined, leading to projective representations of restricted unitary groups.
Syllabus
Karl-Hermann Neeb - Covariant projective representations of Hilbert--Lie groups
Taught by
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)