This course is designed for master/PhD students in Maths and Physics. In general, it is expected that the construction of induced modules and their homomorphisms, closely linked to to the invariant linear differential operators in geometric categories, will allow for an analog in the supersymmetric setup. The lectures will focus on the necessary background and aim at bringing the audience close to the current research in this hot area.
Through the course, we will cover notions from the following topics:
1) Structure theory of semi-simple Lie algebras and representation theory (definitions, examples, basic results) ;
2) Lie superalgebras and enveloping algebras (definitions, examples, basic results) ;
3) Homogeneous spaces, Grassmannians, principal bundles, induced bundles, induced modules;
4) Material from Category theory and Scheme theory;
5) Supermanifolds, Supergroups;
6) Invariant Differential Operators, Verma modules;
7) Invariant Super Differential Operators, induced modules in the supersymmetric setup.
Part of blackboards from the first week meeting - sorry for not pushing the recording button (and skipping the second set of boards).
In the second week, we have got the boards from the online lecture by Ioannis:
and about the first hour of the recording (then the unattended computer decided to reboot ...):
The boards from the third lectures:
and the video of the same lecture: