Introduction to Lie Groups II Prof. Alessandra Iozzi (E-Mail)   Course Time: Thursday, 10-12 Place: Grosser Hörsaal, Mathematisches Institut Starting date: Thursday, 13th April 2006. Exercise sessions Time: To be decided, possibly every Thursday 12-13 Place: Grosser Hörsaal, Mathematisches Institut Starting date: Thursday, 20th April 2006 Prerequisites Basic notions about the structure of Lie groups Content Lie groups in the diffeomorphism group of a manifold, homogeneous spaces, invariant volume forms, invariant metrics Linear algebraic groups: hands-on approach, Borel density theorem Representation theory of semisimple Lie groups: Weyl's theorem on the semisimplicity of finite dimensional representations and Howe--Moore's theorem on the vanishing at infinity of matrix coefficients of unitary representations Intended audience Beginning graduate students. References: A. Sagle & R. Walde, Introduction to Lie groups and Lie algebras, Academic Press, 1973 F. Warner, Foundations of differentiable manifolds and Lie groups, Springer, 1971 H. Samelson, Notes on Lie algebras, Springer, 1990 S. Helgason, Differential geometry, Lie groups and symmetric spaces, Academic Press, 1978 A. Knapp, Lie groups, Lie algebras and cohomology, Princeton University Press R. Zimmer, Ergodic theory and semisimple groups, Birkhäuser, 1985 Exercise sheets Exercises will be assigned at first during the lectures.

Last modification: 31st Mar. 2006