Introduction to geometric representation theory
MATH-686 / 2 crédits
Enseignant: Wyss Dimitri Stelio
Langue: Anglais
Remark: Participants are required to solve exercices and present them in class during the whole semester.
Frequency
Every year
Summary
This course presents geometric constructions of irreducible representations of semi-simple Lie Algebras and their Weyl groups by means of Springer theory.
Content
In this course we study (symplectic) manifolds and algebraic varieties associated with complex semi-simple groups. To goal is to use these geometric objects and in particular their (co)homology go construct irreducible representations of the semi-simple group and its Weyl group.
The main reference for the course is the book "Representation Theory and Complex Geometry" by N. Criss and V. Ginzburg.
The topics we cover include:
- Symplectic geometry
- C*-actions on algebraic varieties
- Borel-Moore homology
- Springer Resolution
- Weyl group representations
- Universal envelopping algebras
- Hecke algebras
Note
By the end of the course, the student must be able to understand basic concepts in geometric representation theory and solve concrete problems about representations of semi-simple algebraic groups.
Learning Prerequisites
Required courses
Some background in algebraic geometry, differential geometry and linear algebraic groups.
Resources
Bibliography
"Representation Theory and Complex Geometry" by N. Criss and V. Ginzburg.
Dans les plans d'études
- Forme de l'examen: Pendant le semestre (session libre)
- Matière examinée: Introduction to geometric representation theory
- Cours: 28 Heure(s)