Publication: Research - peer-review › Journal article

- Henning Haahr AndersenHenning Haahr AndersenDenmark
- Volodymyr MazorchukVolodymyr MazorchukUppsala UniversitetSweden

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.

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 language | English |
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Journal | European Mathematical Society. Journal |

Volume | 17 |

Issue number | 2 |

Pages (from-to) | 405-431 |

Number of pages | 27 |

ISSN | 1435-9855 |

DOIs | |

State | Published - Feb 2015 |

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ID: 84970617