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Category 𝒪 for quantum groups

Henning Haahr AndersenVolodymyr Mazorchuk — 2015

Journal of the European Mathematical Society

In this paper we study the BGG-categories 𝒪 q associated to quantum groups. We prove that many properties of the ordinary BGG-category 𝒪 for a semisimple complex Lie algebra carry over to the quantum case. Of particular interest is the case when q is a complex root of unity. Here we prove a tensor decomposition for both simple modules, projective modules, and indecomposable tilting modules. Using the known Kazhdan-Lusztig conjectures for 𝒪 and for finite dimensional U q -modules we are able to determine...

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