Reading group on Lie Theory organized as part of the Graduate directed reading for undergraduates.
- Mentors (email)
-
Abhik Pal
Runqiu Xu
Suhas Gondi
- Meeting time and location
- Wed 2:00-3:00pm, HSS 4025
- References
- • John Stillwell, Naive Lie Theory
- • William Fulton and Joe Harris, Representation Theory: A First Course
- • James Humphreys, Introduction to Lie Algebras and Representation Theory
- • John M. Lee, Introduction to Smooth manifolds (2ed)
Schedule
Each session will consist of short talks by the participants on the assigned reading for that week. We will recommend some exercises to discuss after the talk.
- Apr 12: Some basic examples
-
Reading: Sec 1.3, 1.5, 2.1, 2.3, 2.4, 2.5 (Stillwell)
Exercises: 1.5.3, 1.5.5, 2.3.5, 2.6.4 (Stillwell)
Speaker: Matthew Yao - Apr 19: The exponential map
-
Reading: Sec 3.2 3.3, 3.5, Ch 4 (Stillwell)
Optional Reading: Ch 7 (Lee)
Exercises: 3.2.1, 4.4.2, 4.5.4 (Stillwell)
Speaker: Aiyang Lu - Apr 26: Tangent space and Lie algebras
-
Reading: Ch 5, 6 (Stillwell)
Speaker: Fuxiang Yang - May 3: Representation theory of the symmetric group
-
Reading: Sec 1.1, 1.2, 2.1, 4.1, 4.2 (Fulton and Harris)
Speaker: Frederick Rajasekaran - May 10: Representations of \(\mathfrak{sl}_2(\mathbf C)\)
-
Reading: Ch 11 (Fulton and Harris), Sec II.7 (Humphreys)
Exercises: Ex. 11.10, 11.13 (Fulton and Harris)
Optional exercises: Ex. 11.11, 11.14 (Fulton and Harris)
Speaker: Kaoru Otsuka (notes) - May 17: Generalization to an arbitrary semi-simple Lie algebra
-
Reading: Ch 12, 14 (Fulton and Harris)
Speaker: Andrew Paul - May 24: Representations of \(\mathfrak{sl}_3\mathbf{C}\)
-
Reading: Ch 13 (Fulton and Harris)
Speaker: Matthew Yao - May 31: Final presentation preparation