Title of the course: Representation Theory of Complex Lie Algebras
Instructor: Assoc. Prof. Mustafa Kalafat
Institution: Nesin Matematik Köyü (NMK)
Dates: 7-11 September 2020
Prerequisites: Linear Algebra, Lie groups and Lie algebras.
Level: Graduate advanced undergraduate
Abstract: In this lecture series we give an introduction to the representation theory of some complex Lie algebras. We review Lie groups, Lie algebras, Cartan subalgebra, Root systems. Then, starting from concrete examples we will work on sl(2,C), sl(3,C), sl(4,C) and finally sl(n,C) and their representations. We also go into their geometric interpretations. Also spend time on sp(2n,C) and so(m,C) if time permits.
Textbook:
1. Fulton, William; Harris, Joe – Representation theory. A first course. Graduate Texts in Mathematics, 129. Readings in Mathematics. Springer-Verlag, New York, 1991. xvi+551 pp. ISBN: 0-387-97527-6
2. Anthony W. Knapp. Lie groups beyond an introduction, volume 140 of Progress in Mathematics. Birkhauser Boston, Inc., Boston, MA, second edition, 2002.
Language: EN/TR