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Category O for quantum groups

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  • Henning Haahr Andersen, Denmark
  • Volodymyr Mazorchuk, Uppsala University, Sweden
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.
Original languageEnglish
JournalJournal of the European Mathematical Society
Volume17
Issue2
Pages (from-to)405-431
Number of pages27
ISSN1435-9855
DOIs
Publication statusPublished - Feb 2015

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