Home » Second Level Degree » Courses » REPRESENTATION THEORY OF GROUPS

Second Level Degree in Mathematics

Jump second level menu

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)

Move Up ▲

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

Textbooks (and optional supplementary readings)

Torna su ▲