Loop groups and string topology

zbMATH Open1137.22012arXiv0802.3719MaRDI QIDQ5423243

Thomas Schick

Publication date: 23 October 2007

Abstract: Survey article on loop groups and their representations, following a course of three lectures held at the summer school "algebraic groups" at the Georg-August-Universitaet zu Goettingen, June 27--July 13, 2005. We discuss loop groups, their central extensions, and positive energy representations.

Full work available at URL: https://arxiv.org/abs/0802.3719

zbMATH Keywords

homogeneous spacesGrassmanniansloop groupsinfinite-dimensional Lie groupscompact Lie groupsrepresentations of loop groups

Mathematics Subject Classification ID

Grassmannians, Schubert varieties, flag manifolds (14M15) Loop groups and related constructions, group-theoretic treatment (22E67) Infinite-dimensional Lie groups and their Lie algebras: general properties (22E65) Compact groups (22C05) Homogeneous complex manifolds (32M10) Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) (22E47)

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