$p$-filtrations of dual Weyl modules

Henning Haahr Andersen

$p$-filtrations of dual Weyl modules

Representation Theory 2019-05-21 v2

Authors: Henning Haahr Andersen

Abstract

Let $G$ be a semisimple algebraic group over a field of characteristic $p > 0$ . We prove that the dual Weyl modules for $G$ all have $p$ -filtrations when $p$ is not too small. Moreover, we give applications of this theorem to $p^n$ -filtrations for $n > 1$ , to modules containing the Steinberg module as a tensor factor, and to the Donkin conjecture on modules having $p$ -filtrations.

Keywords

semisimple algebraic group dual Weyl module p-filtration Steinberg module Donkin conjecture

Cite

@article{arxiv.1810.04052,
  title  = {$p$-filtrations of dual Weyl modules},
  author = {Henning Haahr Andersen},
  journal= {arXiv preprint arXiv:1810.04052},
  year   = {2019}
}

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