Lie algebras and representation theory, fall 2013

Lecturer

Jouko Mickelsson

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.

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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