Lecture 1: Continuous Representations of Topological Groups
Lecture 2: \(K\)-finite Vectors and Matrix Coefficients
Problem set 1 due
Lecture 3: Algebras of Measures on Locally Compact Groups
Lecture 4: Plancherel Formulas, Dirac Sequences, Smooth Vectors
Problem set 2 due
Lecture 5: Admissible Representations and (\(\mathfrak{g}\), \(K\))-Modules
Lecture 6: Weakly Analytic Vectors
Problem set 3 due
Lecture 7: Infinitesimal Equivalence and Globalization
Lecture 8: Highest Weight Modules and Verma Modules
Problem set 4 due
Lecture 9: Representations of \(SL_2\mathbb{R}\)
Lecture 10: The Chevalley Restriction Theorem and the Chevalley-Shephard-Todd Theorem
Problem set 5 due
Lecture 11: Proof of the Chevalley-Shephard-Todd Theorem, Part I
Lecture 12: Proof of the Chevalley-Shephard-Todd Theorem, Part II
Problem set 6 due
Lecture 13: Kostant’s Theorem
Lecture 14: Harish-Chandra Isomorphism, Maximal Quotients
Problem set 7 due
Lecture 15: Category \(\mathcal{O}\) of \(\mathfrak{g}\)-Modules, Part I
Lecture 16: Category \(\mathcal{O}\) of \(\mathfrak{g}\)-Modules, Part II
Problem set 8 due
Lecture 17: The Nilpotent Cone of \(\mathfrak{g}\)
Lecture 18: Maps of Finite Type, the Duflo-Joseph Theorem
Problem set 9 due
Lecture 19: Principal Series Representations
Lecture 20: BGG Reciprocity and the BGG Theorem
Problem set 10 due
Lecture 21: Multiplicities in Category \(\mathcal{O}\)
Lecture 22: Projective Functors, Part I
Problem set 11 due
Lecture 23: Projective Functors, Part II
Lecture 24: Applications of Projective Functors, Part I
Problem set 12 due
Lecture 25: Applications of Projective Functors, Part II
Lecture 26: Representations of \(SL_2\mathbb{C}\)
Problem set 13 due
Lecture 27: Geometry of Complex Semisimple Lie Groups
Lecture 28: D-Modules, Part I
Problem set 14 due
Lecture 29: The Beilinson-Bernstein Localization Theorem
Lecture 30: D-Modules, Part II
Problem set 15 due
Lecture 31: Applications of D-modules to Representation Theory
Problem set 16 due
