Second Level Degree in Mathematics
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REPRESENTATION THEORY OF GROUPS - 6 CFU
Teacher
Francesco Esposito
Scheduled Period
I Year - 2 Semester | 02/03/2020 - 12/06/2020
Hours: 48 (16 esercitazione, 32 lezione)
Prerequisites
Basic notions in linear algebra and group theory.
Target skills and knowledge
The student will learn the basic notions on complex representations of finite groups and the classification of complex semisimple Lie algebras.
Examination methods
Written exam
Assessment criteria
Exams will be evaluated on basis of their completeness, correctness and exactness.
Course contents
Representations. Irreducible representations. Maschke's theorem. Orthogonality of characters. Induced representations. Frobenius reciprocity. Rappresentazioni Indotte, formual di Mackey. Reciprocita' di Frobenius. Frobenius-Scur Indicator. Compact groups. Linear algebraic groups and their Lie algebras. Solvable, nilpotent and semisimple Lie algebras. Cartan's criterion. Killing form. Weyl's theorem. Root space decomposition. Root systems. Classification of semisimple Lie algebras. Universal enveloping algebras. Finite dimensional irreducible representations of a semisimple Lie algebra.
Planned learning activities and teaching methods
Classroom lectures. In the course webpage students can find exercises to solve.
Additional notes about suggested reading
We will also use a few pages from these Lecture Notes by Alexander Kleschchev
http://darkwing.uoregon.edu/~klesh/teaching/AGLN.pdf