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Durham University

Centre for Particle Theory

Group Theory

12 lectures Dr. D. Dorigoni

This course concerns various aspects of the continuous groups which appear in High Energy Physics and Conformal Field Theory. Lie groups and algebras and their representations will be introduced with relevant examples, before turning to the general classification of semisimple Lie algebras provided by Dynkin diagrams.

Outline of the course

U(n), SO(n) and their representations.
Simple Lie groups and algebras.
The classification of semisimple Lie algebras.
Representations: roots and weights.

Books for the course

H. Georgi, Lie Algebras in Particle Physics (Perseus Books 1999)
R. Cahn, Semi Simple Lie Algebras And Their Representations (Frontiers In Physics Series Volume 59 or here)
H. Samelson, Notes on Lie Algebras (Springer 1990)
J. Fuchs and C. Schweigert, Symmetries, Lie Algebras and Representations (CUP 1997)
W. Fulton and J. Harris, Representation Theory: A first course (Springer Science & Business Media, 1991)