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** Math 771 (Fall 2017): Lie Groups and Representation Theory **

** Instructor: ** Mahir Bilen Can

**Office: ** Gibson Hall 318 A

**Office Hours: ** By appointment

**Email: ** mcan@tulane.edu

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** What is a Lie group?
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A Lie group is a differentiable manifold with a group structure where the multiplication and inverse
operations are differentiable maps of manifolds. A representation of a Lie group M is just another way of seeing M as
a group of linear transformations.
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** What is this course about?
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- Definitions, examples, and basic properties of Lie groups and Lie algebras;
- Function theory on (compact) Lie groups;
- Structure of Lie groups;
- Basic representation theory of compact Lie groups.

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** Textbooks:
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- Main textbook: Representations of compact Lie groups by Theodor Brocker and Tammo tom Dieck.
- Supplementary: Differential geometry, Lie groups, and symmetric spaces by Sigurdur Helgason.
- Supplementary: The structure of compact groups by Karl H. Hofmann and Sidney A. Morris.

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** Grading:
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There will be four take-home exams to be collected within seven days after their assignments. The (rough) dates of these assignments are
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- September 29 (Friday),
- October 30 (Monday),
- November 20 (Monday),
- December 8 (Friday).