A q-Analogue of Kempf's vanishing theorem

Steen Ryom-Hansen

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arxiv 0905.0236 v1 pith:YDL3PDAW submitted 2009-05-03 math.RT math.AG

A q-Analogue of Kempf's vanishing theorem

Steen Ryom-Hansen This is my paper

classification math.RT math.AG

keywords kempftheoremvanishinganalogonandersenbasiscrystaldeep

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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.

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Proves nonsemisimple quantum Howe duality for Sp(2n) and SL(2) on exterior algebra of type C, with character formulas and canonical bases.