Tilting modules in category and sheaves on moment graphs

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• 作者：Johannes K¨¹bel
• 关键词：Representation theory ; Category O
• 刊名：Journal of Algebra
• 出版年：2012
• 出版时间：1 December, 2012
• 年：2012
• 卷：371
• 期：Complete
• 页码：559-576
• 全文大小：254 K

文摘

We describe tilting modules of the deformed category over a semisimple Lie algebra as certain sheaves on a moment graph associated to the corresponding block of . We prove that they map to Braden-MacPherson sheaves constructed along the reversed Bruhat order under Fiebig?s localization functor. By this means, we get character formulas for tilting modules and explain how Soergel?s result about the Andersen filtration gives a Koszul dual proof of the semisimplicity of subquotients of the Jantzen filtration.