Loewy structure of $G_1T$-Verma modules of singular highest weights

Noriyuki Abe; Masaharu Kaneda

Loewy structure of $G_1T$-Verma modules of singular highest weights

Representation Theory 2015-04-02 v2

Authors: Noriyuki Abe , Masaharu Kaneda

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 $G_1T$ -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 $G_1T$ -characters hold.

Keywords

reductive algebraic groups frobenius kernel verma modules loewy structure singular highest weights kazhdan-lusztig polynomials lusztig conjecture

Cite

@article{arxiv.1501.07029,
  title  = {Loewy structure of $G_1T$-Verma modules of singular highest weights},
  author = {Noriyuki Abe and Masaharu Kaneda},
  journal= {arXiv preprint arXiv:1501.07029},
  year   = {2015}
}

Comments

12 pages

Loewy structure of $G_1T$-Verma modules of singular highest weights

Abstract

Keywords

Cite

Comments

Related papers