Loewy structure of $G_{1}T$-Verma modules of singular highest weights

Abstract

Let $G$ be a reductive algebraic group over an algebraically closed field of positive characteristic, $G_1$ the Frobenius kernel of $G$, and $T$ a maximal torus of $G$. We show that the $G_{1}T$-Verma modules of singular highest weights are all rigid, determine their Loewy length, and describe their Loewy structure using the periodic Kazhdan-Lusztig $Q$-polynomials. We assume that the characteristic of the field is large enough that, in particular, Lusztig's conjecture for the irreducible $G_{1}T$-characters hold.

12 pages

References in corpus (1)

• Localization of modules for a semisimple Lie algebra in prime characteristic