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Category O for quantum groups
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
2015 (English)In: Journal of the European Mathematical Society (Print), ISSN 1435-9855, E-ISSN 1435-9863, Vol. 17, no 2, 405-431 p.Article in journal (Refereed) Published
Abstract [en]

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 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 all irreducible characters as well as the characters of all indecomposable tilting modules in O-q. As a consequence, we also recover the known result that the generic quantum case behaves like the classical category O.

Place, publisher, year, edition, pages
2015. Vol. 17, no 2, 405-431 p.
Keyword [en]
Quantized highest weights modules, specialization at roots of unity, tensor decompositions, tilting modules
National Category
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-252743DOI: 10.4171/JEMS/506ISI: 000352495900005OAI: oai:DiVA.org:uu-252743DiVA: diva2:811170
Available from: 2015-05-11 Created: 2015-05-11 Last updated: 2017-12-04Bibliographically approved

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Mazorchuk, Volodymyr

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