Ben Wilson (University of Sydney)
Friday 13rd October, 12.05-12.55pm, Carslaw 373Highest-weight theory for Lie algebras of truncated currentsLet g be a Lie algebra over a field k, and fix a positive integer N. The Lie algebra g ⊗_{k} k[t]/t^{N+1}k[t] is called a truncated current Lie algebra. In this talk we explore highest-weight theories for such Lie algebras, and discuss a recent finding that provides a reducibility criterion for the Verma modules of a theory when g is either a semisimple finite-dimensional Lie algebra, the Virasoro algebra, a Heisenberg algebra, or an affine Kac-Moody Lie algebra. Examples are considered to illustrate the general picture, which is remarkably uniform. |