Lie groups, Lie algebras, and their representations
Instructor: Joel Kamnitzer, jkamnitz@gmail.com
Lectures: Mondays and Wednesdays 11:00 - 12:30, BURN 1234
There will be no class on October 3 (election), but we do have class on Thursday October 13.
Office: BURN 1107
Office Hours: Tuesday 10:00 - 12:00
Grading scheme:
Syllabus:
Lie groups, examples and general theory.
Structure theory of Lie algebras.
Classification of semisimple Lie algebras.
Representation theory of semisimple Lie algebras and compact Lie groups.
Algebraic groups.
Flag varieties and the Borel-Weil theorem.
Quantum groups and crystals.
Homework:
Assignment 1 (pdf, tex) due Wednesday September 21.
Assignment 2 (pdf, tex) due Wednesday October 5.
Assignment 3 (pdf, tex) due Wednesday October 26.
Assignment 4 (pdf, tex) due Wednesday November 9.
Assignment 5 (pdf, tex) due Wednesday November 30.
Resources:
Introduction to Lie Groups and Lie Algebras by Kirillov. This will be my main reference.
Berkeley Lectures on Lie groups and quantum groups. There is a lot in here, but it is a bit of a mess.
Allen Knutson's notes (this is from the course I took in my first year in grad school). A bit of a mess, but you definitely see the influence in my lectures.
Representations of compact Lie groups by Brocker and tom Dieck. As the name implies, this focuses on compact groups.
Symmetry, Representations, and Invariants by Goodman and Wallach. This covers classical groups from an algebraic groups perspective.
Representation theory: A first course by Fulton and Harris. Begins with finite groups, then covers representation theory of semisimple Lie algebras, and at the end does some algebraic geometry.
Complex semisimple Lie algebras by Serre. A beautiful self-contained book.
Representation theory, my own notes from 10 years ago.
Lie groups and Lie algebras, lecture notes by Eckhard Meinrenken.