Rutgers Math 549 - Lie Groups
Course material from previous semesters
Spring 2005
Course material for current semester (Spring, 2008)
Lecturer: Prof. Roe Goodman
Announcements
Office Hours:
MW 4:00-5:00 (and usually Th 2:00-3:00)
Reference books:
The books by Rossmann and Goodman-Wallach have been put on reserve in
the math library.
Text: Selected chapters from the new book Symmetry, Representations, and Invariants by Roe Goodman and Nolan R. Wallach (to appear). These chapters will be available for downloading from this page during the first and second week of the term. The corrected third printing (2003) of the previous book Representations and Invariants of the Classical Groups is available from Cambridge University Press (ISBN 0-521-66348-2) and other booksellers.
Description and Prerequisites: This course will be an introduction to Lie groups and algebraic groups. The prerequisites are real analysis, linear algebra, and elementary topology. Students who took Prof. Buch's course 640:556 Representation Theory and are interested in learning more Lie theory will find this course provides a natural continuation and alternate points of view. However, no prior knowledge of Lie algebras, Lie groups, or representation theory will be assumed.
Course Outline:
- The classical linear groups (real and complex forms)
- Closed subgroups of GL(n) as Lie groups
- Linear algebraic groups and rational representations
- Structure of complex classical groups: maximal torus, roots, adjoint representation, Weyl group
- Highest weight theory for representations of semisimple Lie algebras
- Complete reducibility of representations of semisimple Lie algebras and classical groups
Grading: There are graded
homework exercises that are due every two weeks during the term.
(revised March 20)
Lectures: Here is a detailed
syllabus
(revised April 17)
Roe Goodman / goodman "at" math "dot" rutgers "dot" edu / Revised May 1, 2008
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