Friday, May 20 2022
11:30 - 12:30

IMSc Webinar

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

Apoorva Khare

Indian Institute of Science

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Meeting ID: 912 8892 8049
Passcode: Macdonald

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", and we end by explaining BGG resolutions and Weyl-Kac type character formulas, for these modules in certain cases. (Joint with G.V.K. Teja and with Gurbir Dhillon.)

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