Thursday, June 2 2022
11:30 - 12:30

IMSc Webinar

Higher order Verma modules, and a positive formula for all highest weight modules - 2

Apoorva Khare

Indian Institute of Science

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). To keep this talk self-contained, we begin by recalling the notation, "higher order holes", and weight formulas for general $V$ from the previous lecture, along with some examples. We then define "higher order Verma modules", and explain BGG resolutions and Weyl-Kac type character formulas for them in certain cases. (Joint with G.V.K. Teja.)

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