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Math 549 - Lie Groups; Rutgers, New Brunswick

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:

  1. The classical linear groups (real and complex forms)
  2. Closed subgroups of GL(n) as Lie groups
  3. Linear algebraic groups and rational representations
  4. Structure of complex classical groups: maximal torus, roots, adjoint representation, Weyl group
  5. Highest weight theory for representations of semisimple Lie algebras
  6. 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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This page was last updated on June 03, 2008 at 06:26 pm and is maintained by webmaster@math.rutgers.edu