Super Quantization

Explore super quantization in this 50-minute lecture by Rita Fioresi from the Universita' di Bologna, part of the Workshop on Supergeometry and Bracket Structures in Mathematics and Physics. Delve into the functor of points approach, super Harish-Chandra pairs, and representations of supergroups. Examine hermitian and super hermitian products, unitary representations of Lie superalgebras, and infinitesimal Harish-Chandra highest weight unitary representations. Investigate admissible positive systems, geometric realizations of HC unitary representations, super Iwasawa decomposition, and geometric quantization. Gain insights into the intricate world of super quantization and its applications in mathematics and physics.

Intro
The functor of points approach
Super Harish-Chandra pairs (SHCP)
Representations of Supergroups
Hermitian and Super Hermitian products V: complex super vector space Definition() is a super hermitian product on Vif
Unitary representations of Lie superalgebras
Important case: Harish-Chandra representations
Infinitesimal Harish-Chandra highest weight unitary representations
Admissible Positive Systems
Geometric realizations of HC Unitary Representations
Super Iwasawa Decomposition
Geometric Quantization
Super Quantization/2