18.757 | Fall 2023 | Graduate

Representations of Lie Groups

Lecture Notes

pdf
1 MB
18.757 F23 Full Lecture Notes: Representations of Lie Groups
pdf
460 kB
18.757 F23 Lecture 01: Continuous Representations of Topological Groups
pdf
352 kB
18.757 F23 Lecture 02: K-finite Vectors and Matrix Coefficients
pdf
422 kB
18.757 F23 Lecture 03: Algebras of Measures on Locally Compact Groups
pdf
384 kB
18.757 F23 Lecture 04: Plancherel Formulas, Dirac Sequences, Smooth Vectors
pdf
381 kB
18.757 F23 Lecture 05: Admissible Representations and (g, K)-Modules
pdf
354 kB
18.757 F23 Lecture 06: Weakly Analytic Vectors
pdf
405 kB
18.757 F23 Lecture 07: Infinitesimal Equivalence and Globalization
pdf
388 kB
18.757 F23 Lecture 08: Highest Weight Modules and Verma Modules
pdf
425 kB
18.757 F23 Lecture 09: Representations of SL2(R)
pdf
359 kB
18.757 F23 Lecture 10: The Chevalley Restriction Theorem and the Chevalley-Shephard-Todd Theorem
pdf
378 kB
18.757 F23 Lecture 11: Proof of the Chevalley-Shephard-Todd Theorem, Part I
pdf
438 kB
18.757 F23 Lecture 12: Proof of the Chevalley-Shephard-Todd Theorem, Part II
pdf
430 kB
18.757 F23 Lecture 13: Kostant's Theorem
pdf
347 kB
18.757 F23 Lecture 14: Harish-Chandra Isomorphism, Maximal Quotients
pdf
373 kB
18.757 F23 Lecture 15: Category O of g-Modules, Part I
pdf
417 kB
18.757 F23 Lecture 16: Category O of g-Modules, Part II
pdf
370 kB
18.757 F23 Lecture 17: The Nilpotent Cone of g
pdf
359 kB
18.757 F23 Lecture 18: Maps of Finite Type, the Duflo-Joseph Theorem
pdf
373 kB
18.757 F23 Lecture 19: Principal Series Representations
pdf
375 kB
18.757 F23 Lecture 20: BGG Reciprocity and the BGG Theorem
pdf
368 kB
18.757 F23 Lecture 21: Multiplicities in Category O
pdf
369 kB
18.757 F23 Lecture 22: Projective Functors, Part I
pdf
374 kB
18.757 F23 Lecture 23: Projective Functors, Part II
pdf
370 kB
18.757 F23 Lecture 24: Applications of Projective Functors, Part I
pdf
364 kB
18.757 F23 Lecture 25: Applications of Projective Functors, Part II
pdf
362 kB
18.757 F23 Lecture 26: Representations of SL2(C)
pdf
430 kB
18.757 F23 Lecture 27: Geometry of Complex Semisimple Lie Groups
pdf
373 kB
18.757 F23 Lecture 28: D-Modules, Part I
pdf
353 kB
18.757 F23 Lecture 29: The Beilinson-Bernstein Localization Theorem
pdf
440 kB
18.757 F23 Lecture 30: D-Modules, Part II
pdf
416 kB
18.757 F23 Lecture 31: Applications of D-modules to Representation Theory

Course Info

Instructor
Departments
As Taught In
Fall 2023
Level
Graduate
Topics
Learning Resource Types
Online Textbook
Lecture Notes
Problem Sets
Download Course
MIT Open Learning
Over 2,500 courses & materials
Freely sharing knowledge with learners and educators around the world. Learn more
© 2001–2024 Massachusetts Institute of Technology
Accessibility
Creative Commons License
Terms and Conditions
Proud member of:
© 2001–2024 Massachusetts Institute of Technology