S. Ryom-Hansen, “A <nobr>$q$</nobr>-analogue of Kempf's vanishing theorem”, Mosc. Math. J., 2003, Volume 3, Number 1,Pages <nobr>173

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A $q$-analogue of Kempf's vanishing theorem

S. Ryom-Hansen

Department of Mathematical Sciences, University of Copenhagen

Abstract: We use deep properties of Kashiwara's crystal basis to show that the induction functor $H_k^0(-)$ introduced by Andersen, Polo and Wen satisfies an analogon of Kempf's vanishing theorem for k a field.

Key words and phrases: Kempf Vanishing, Quantum groups, crystal basis, $H_k^0(-)$, Demazure modules.

MSC: 17B37, 20G42

Received: October 16, 2001

Language: English

DOI: 10.17323/1609-4514-2003-3-1-173-187