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Course Descriptions

16:640:549 - Lie Groups

Vladimir Retakh

Text:

Fulton, Harris "Representation Theory"

Prerequisites: 

Real Analysis, Linear Algebra, and Elementary Topology. No prior knowledge of Lie algebras, Lie groups, or representation theory will be assumed.

Description:

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
    

Sections Taught This Semester:

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Department of Mathematics

Department of Mathematics
Rutgers University
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