Apoorva Khare
Indian Institute of Science
April 3, 2025
Higher order Verma modules: weights and their multiplicities: 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.)
Indian Institute of Science
April 3, 2025
Higher order Verma modules: weights and their multiplicities: 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.)