Lecture 1: Representations of \(GL_n\), I

Lecture 2: Representations of \(GL_n\), II

*Problem set 1 due*

Lecture 3: Representations of \(GL_n\), III

Lecture 4: Fundamental and Minuscule Weights

*Problem set 2 due*

Lecture 5: Fundamental Representations of Classical Lie Algebras

Lecture 6: Maximal Root, Exponents, Coxeter Numbers, Dual Representations

*Problem set 3 due*

Lecture 7: Differential Forms, Partitions of Unity

Lecture 8: Integration on Manifolds

*Problem set 4 due*

Lecture 9: Representations of Compact Lie Groups

Lecture 10: Proof of the Peter-Weyl Theorem

*Problem set 5 due*

Lecture 11: Representations of Compact Topological Groups

Lecture 12: The Hydrogen Atom, I

*Problem set 6 due*

Lecture 13: The Hydrogen Atom, II

Lecture 14: Forms of Semisimple Lie Algebras over an Arbitrary Field

*Problem set 7 due*

Lecture 15: Classification of Real Forms of Semisimple Lie Algebras

Lecture 16: Real Forms of Exceptional Lie Algebras

*Problem set 8 due*

Lecture 17: Classification of Connected Compact and Complex Reductive Groups

Lecture 18: Maximal Tori in Compact Groups, Cartan Decomposition

*Problem set 9 due*

Lecture 19: Topology of Lie Groups and Homogeneous Spaces, I

Lecture 20: Topology of Lie Groups and Homogeneous Spaces, II

*Problem set 10 due*

Lecture 21: Topology of Lie Groups and Homogeneous Spaces, III

Lecture 22: Levi Decomposition

*Problem set 11 due*

Lecture 23: The Third Fundamental Theorem of Lie Theory

Lecture 24: Ado’s Theorem

*Problem set 12 due*

Lecture 25: Borel Subgroups and the Flag Manifold of a Complex Reductive Lie Group

*Problem set 13 due*