Category O for quantum groups

• 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.

Subject headings

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Keyword

Quantized highest weights modules

specialization at roots of unity

tensor decompositions

tilting modules

Publication and Content Type

ref (subject category)

art (subject category)