Algebra Seminar

Weight modules for current algebras
lundi, 3 avril 2017 - 1:10 pm1:40 pm
Lieu
Numéro de salle: 
HP 4325
Lieu hors campus: 
Carleton University
Inscription
Inscription requise: 
Non
Frais de participation: 
Sans frais
Organisateur de l'événement : 
Langue de l'événement : 

 

SPEAKER: Michael Lau (Laval) DATE: Monday, April 3, 2017 TIME: 1:10 pm ROOM: HP 4325 (Carleton) ABSTRACT:

Affine Lie algebras burst onto the mathematical scene in the late 1960s as the most important infinite-dimensional examples of the newly discovered Kac-Moody algebras. From the beginning, it was understood that they have a powerful alternative interpretation as extensions of loop algebras, families of functions from the circle to finite-dimensional Lie algebras. By replacing the circle with other smooth manifolds or algebraic varieties, we obtain a large class of Lie algebras, known as current algebras. They appear in geometry and many applications, including singularity theory, gauge theory, soliton equations, and exactly solvable models.

After introducing these algebras, we will discuss the classification of simple weight modules (with finite-dimensional weight spaces) for current algebras. The modules are constructed using parabolic induction from admissible representations of Levi subalgebras, and their classification reduces to Mathieu's results on admissible weight modules for reductive Lie algebras.