### Math 8271-8272: Lie Groups and Lie Algebras (Fall, 2013; Spring, 2014)

#### Instructor:

Dr. Dihua Jiang
Office: VinH 224, Telephone: 625--7532, E-mail: dhjiang@math.umn.edu
#### Text, Lecture, Course Description:

Textbook: Symmetry, Representations, and Invariants (Springer GTM 255, 2009) by R. Goodman; N. Wallach

Lecture: Mon-Wed-Fri at 09:05am--09:55am, Vincent Hall 311
Office Hours: 3:00-4:00pm MW; or by appointment

Course Description:

This is a two semester course on basic Lie Theory. We follow the textbook closely and discuss:

(1) Basic Structures of Complex Lie groups and Lie algebras;

(2) Representatin Theory of finite, Lie groups and Lie algebras;

(3) Invariants: polynomial type, tensor type;

(4) Particular realizations of representations and invariants.

The materials covered in this year-long course are fundamental to many research areas in modern mathematics.

It is definitely important for students who intend to study Algebra, Combinatorics, Automorphic Forms,

Mathematical Physics, and any Mathematics with group actions.

Homework Problems will be assigned, but No Exams are required.