Higher order Verma modules, and a positive formula for all highest weight modules - talk 1

Abstract: We study weights of highest weight modules $V$ over a Kac-Moody algebra $\mathfrak{g}$ (one may assume this to be $\mathfrak{sl}_n$ throughout the talk, without sacrificing novelty). We begin with several positive weight-formulas for arbitrary non-integrable simple modules, and mention the equivalence of several "first order" data that helps prove these formulas. We then discuss the notion of "higher order holes" in the weights, and use these to present two positive weight-formulas for arbitrary modules $V$. One of these is in terms of "higher order Verma modules". (Joint with G.V.K. Teja and with Gurbir Dhillon.)

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.