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.