Speaker: Apoorva Khare
Date: April 03, 2025
Affiliation: Indian Institute of Science

Abstract: Let g be a complex semisimple (or Kac-Moody) Lie algebra. Following D.N. Verma's seminal thesis and work of J. Lepowsky, we introduce a class of universal highest weight g-modules which we term "higher-order Verma modules". We then discuss their universality vis-a-vis weight-sets, and in some cases present formulas for their characters ("higher order Weyl character formula") and even resolutions. We end by discussing the log-concavity of their weight multiplicities; in first-order this extends recent work of J. Huh et al. (Partly joint with G.V.K. Teja, and partly with J. Matherne and A. St.Dizier.)