uu.seUppsala University Publications
Change search
ReferencesLink to record
Permanent link

Direct link
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
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: 2016-02-17Bibliographically approved

Open Access in DiVA

No full text

Other links

Publisher's full text

Search in DiVA

By author/editor
Mazorchuk, Volodymyr
By organisation
Algebra and Geometry
In the same journal
Journal of the European Mathematical Society (Print)

Search outside of DiVA

GoogleGoogle Scholar
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Altmetric score

Total: 342 hits
ReferencesLink to record
Permanent link

Direct link