A q-Analogue of Kempf's vanishing theorem

TL;DR

This paper extends Kempf's vanishing theorem to a q-analogue setting using Kashiwara's crystal basis, providing new insights into quantum group representations.

Contribution

It introduces a q-analogue of Kempf's vanishing theorem leveraging deep properties of Kashiwara's crystal basis.

Findings

The induction functor satisfies the q-analogue of Kempf's vanishing theorem.

Deep properties of crystal basis are instrumental in establishing the result.

The work bridges classical and quantum representation theory.

Abstract

We use deep properties of Kashiwara's crystal basis to show that the induction functor $ {H}^0 (-) $ introduced by Andersen, Polo and Wen satisfies an analogon of Kempf's vanishing Theorem.