Higher order Verma modules, and a positive formula for all highest weight modules - talk 3

Abstract: In this final talk, we continue the study of higher order Verma modules and the higher order category $\mathcal{O}^\mathcal{H}$ over a Kac–Moody algebra $\mathfrak{g}$ (one may assume this to be $\mathfrak{sl}_n$ throughout the talk, without sacrificing novelty). After recalling the definitions, we explain how BGG reciprocity fails to hold "on the nose", yet does hold in a modified form over $\mathfrak{g} = \mathfrak{sl}_2^{\oplus n}$. We then explain BGG resolutions and Weyl-Kac type character formulas, for these modules in certain cases. (Joint with G.V.K. Teja.)

combinatoricsrings and algebrasrepresentation theory

Audience: researchers in the topic

( video )

ARCSIN - Algebra, Representations, Combinatorics and Symmetric functions in INdia

Series comments: Timings may vary depending on the time zone of the speakers.