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
