Type: Seminar

Distribution: World

Expiry: 7 Jun 2019

CalTitle1: Ciappara: Tensor products of finite and infinite dimensional representations of semisimple Lie algebras, Part I

Calendar2: 7 Jun 2019 1415-1615

CalLoc2: Carslaw 830

CalTitle2: Ciappara: Tensor products of finite and infinite dimensional representations of semisimple Lie algebras, Part II

Auth: romanova@dora.maths.usyd.edu.au

We begin a two-part study of Bernstein’s classic paper, "Tensor products of finite and infinite dimensional representations of semisimple Lie algebras." In the first week, we define projective functors (in relation to a fixed semisimple Lie algebra \frak{g}) and derive some of their basic properties. These properties are then applied in two directions: first, to find equivalences between interesting categories of modules for \frak{g}; and secondly, to find a correspondence between two-sided ideals of U(\frak{g}) and submodules of Verma modules, with Duflo’s Theorem as a corollary.