Vera Serganova, Lecture I - 20 January 2015
Channel: SNS Sciences
Date: 06/02/2015

Vera Serganova (University of California, Berkeley) - Lecture I
http://www.crm.sns.it/course/4034/

The goal of this minicourse is to review recent results in representation theory of finite-dimensional Lie superalgebras.
Lecture 1 Finite-dimensional Lie superalgebras: classification, examples, highest weight theory, first results about characters.
Lecture 2 Center of universal enveloping superalgebras. Blocks in the category of finite-dimensional representations and category O Stein-Gelfand-Gelfand reciprocity. Weight diagrams.
Lecture 3 Algebraic supergroups. Geometric methods: Borel-Weil-Bott theory, associated variety and odd nilpotent cone.
Lecture 4 Schur-Weyl duality for dierent classical superalgebras. Deligne's theorem and relation with tensor categories.
Lecture 5 Categorification of Fock space via translation functors for superalgebras. Kazhdan-Lusztig-Brundan conjecture for category O in supercase.