Lecture Notes · Lecture Notes
MIT OpenCourseWare
Representations of Lie Groups
Art: Max Brückner (1860 – 1934), Brückner Vielflache Tafel 07 · Public domain
- Instructor
- Prof. Pavel Etingof
- Term
- Fall 2023
- Level
- Graduate
- What's inside
- 32 other files · 3 web pages
- Materials open
- MIT OCW
About this course
Source: MIT OpenCourseWare 18.757 Representations of Lie Groups, Fall 2023, Prof. Pavel Etingof — original course page on ocw.mit.edu ↗. License: CC BY-NC-SA 4.0. Study order: MIT's own listing order, section by section. Taken from MIT's published course files, downloaded from ocw.mit.edu on September 23, 2026. How RedLectern is built.
Materials are grouped the way MIT organized them. A verified, course-wide order has not been established here.
Before you start
Prerequisites are not listed here. Check MIT's own syllabus for this course.
How this course was organized
What's here, and what isn't
- A lecture sequence of 31 items is confirmed. It stays as organized materials rather than a full course order.
Not included here
9 items from the source could not be safely included:
- MIT's page format for this item wasn't recognized clearly enough to place it safely. (9 items)
Materials by section
Grouped by section, as MIT organized them. Not sequenced or ordered.
Problem Sets
Course outline
Lecture Notes · Lecture Notes
18.757 F23 Lecture 02: K-finite Vectors and Matrix Coefficients
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18.757 F23 Lecture 03: Algebras of Measures on Locally Compact Groups
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18.757 F23 Lecture 04: Plancherel Formulas, Dirac Sequences, Smooth Vectors
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18.757 F23 Lecture 05: Admissible Representations and (g, K)-Modules
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18.757 F23 Lecture 06: Weakly Analytic Vectors
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18.757 F23 Lecture 07: Infinitesimal Equivalence and Globalization
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18.757 F23 Lecture 08: Highest Weight Modules and Verma Modules
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18.757 F23 Lecture 09: Representations of SL2(R)
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18.757 F23 Lecture 10: Chevalley Restriction Theorem and Chevalley-Shephard-Todd Theorem
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18.757 F23 Lecture 11: Proof of the Chevalley-Shephard-Todd Theorem, Part I
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18.757 F23 Lecture 12: Chevalley-Shephard-Todd Theorem, Part II
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18.757 F23 Lecture 13: Kostant's Theorem
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18.757 F23 Lecture 14: Harish-Chandra Isomorphism, Maximal Quotients
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18.757 F23 Lecture 15: Category O of g-Modules, Part I
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18.757 F23 Lecture 16: Category O of g-Modules, Part II
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18.757 F23 Lecture 17: The Nilpotent Cone of g
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18.757 F23 Lecture 18: Maps of Finite Type, Duflo-Joseph Theorem
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18.757 F23 Lecture 19: Principal Series Representations
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18.757 F23 Lecture 20: BGG Reciprocity and BGG Theorem
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18.757 F23 Lecture 21: Multiplicities in Category O
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18.757 F23 Lecture 22: Projective Functors, Part I
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18.757 F23 Lecture 23: Projective Functors, Part II
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18.757 F23 Lecture 24: Applications of Projective Functors, Part I
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18.757 F23 Lecture 25: Applications of Projective Functors, Part II
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18.757 F23 Lecture 26: Representations of SL2(C)
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18.757 F23 Lecture 27: Geometry of Complex Semisimple Lie Groups
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18.757 F23 Lecture 28: D-Modules, Part I
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18.757 F23 Lecture 29: The Beilinson-Bernstein Localization Theorem
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18.757 F23 Lecture 30: D-Modules, Part II
Lecture Notes · Lecture Notes
18.757 F23 Lecture 31: Applications of D-modules to Representation Theory
MIT OpenCourseWare, Prof. Pavel Etingof, 18.757 Representations of Lie Groups, Fall 2023.
License: CC BY-NC-SA 4.0 · Edition: Fall 2023 · Open the original course on OCW ↗
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