Representation Theory of Lie groups and Lie algebras
Text:
Combination of
-Fulton-Harris, Representation Theory, a first course
-Humphreys, Introduction to Lie Algebras and Representation Theory
-and notes I will hand out.
format:
students will hand in 3 homework problems each week (more will be
assigned).
One meeting/week will be dedicated to going over homework, the other two
will be lectures. I will also occasionally give supplementary lectures
in a different time slot for those interested in related topics (e.g.,
geometry of rational homogeneous varieties).
grade: based on written and presented homework. (no exams)
Course description:
-Basic definitions, properties, and examples of Lie groups and Lie
algebras
-Representations of the classical groups and algebras
-classification of complex simple Lie algebras
-Existence of representations, Weyl character formula
-Advanced topics as time permits.
Throughout I will emphasize applications (differential geometry,
algebraic
geometry, quantum information theory) although no knowledge of these
areas is
needed for the course.
prerequisite: one semester of graduate algebra or permission of the
instructor
(a strong year long undergraduate course will be sufficient)