Lie algebras and representation theory, fall 2013
Lecturer
Scope
10 sp.
Type
Advanced studies
Prerequisites
Basic algebra and linear algebra
Lectures
Weeks 36-42 and 44-50, Monday 10-12 in room C122 and Tuesday 10-12 in room B321.
Exams
Written examination. NEXT EXAMINATION: January 23, 2014, 4 - 8pm, A111 and B123 in Exactum.
Bibliography
Lecture notes "Mathematical Methods of Physics III" (fall 2012) FYMM3-2012.pdf, Chapters 1-5.
Lecture notes "Lie Algebras and Quantum Groups", lieq.pdf Chapters 1- 4
Additional useful reading: W. Fulton, J. Harris: Representation theory. A first course. Graduate Texts in Mathematics, 129. Readings in Mathematics. Springer-Verlag, New York, 1991. James E. Humphreys: Introduction to Lie Algebras and Representation Theory. Springer-Verlag, GTM 9.
Registration
Did you forget to register? What to do?
Laskuharjoitukset
| Ryhmä | Päivä | Aika | Paikka | Pitäjä |
|---|---|---|---|---|
| 1. | Wednesday | 10-12 | B321 | Eveliina Peltola |
Homework problems
Problem set 1, September 11 Lie1_2013.pdf
Problem set 2, September 18 Lie2_2013.pdf
Problem set 3, September 25 Lie3_2013.pdf
Problem set 4, October 2 Lie4_2013.pdf
Problem set 5, October 9 Lie5_2013.pdf
Problem set 6, October 16: Exercises 1.3.11 - 1.3.15 and 2.1.6 in the lecture notes "Lie algebras and quantum groups"
Problem set 7, October 30: Exercises 2.1.7, 2.1.8, 2.2.12, 2.2.13, 2.2.14 and 2.3.15 in the lecture notes
Problem set 8, November 6: Exercises 2.3.16, 2.3.17, 2.3.18, 2.3.23, 2.3.24 in the lecture notes
Problem set 9, November 13: Exercises 2.3.25, 3.2.5, 3.2.6, 3.2.7, 3.2.8, 3.4.8 in the lecture notes
(see the Appendix A,B: img-Y05125525-0001.pdf img-Y05125545-0001.pdf )
Problem set 10, November 20: Complete the proof of Theorem 3.5.3! Exercises 3.4.9, 3.4.10, 3.5.12, 3.5.13, 3.5.14
Problem set 11, November 27: Exercises 3.6.8, 3.6.10, 3.6.12, 3.6.13, 4.1.6, 4.1.7
Problem set 12, December 4: Exercises 4.3.1, 4.3.5, 4.3.6, 4.4.1, 4.4.3
Problem set 13, December 11: Exercises 4.5.4, 4.5.5, 4.5.7, 4.6.9, 4.6.10