A categorification of finite-dimensional irreducible representations of quantum \mathfraks/2 and their tensor products

• Autores: Igor Frenkel, Mikhail Khovanov, Catharina Stroppel
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 12, Nº. 3-4, 2006, págs. 379-431
• Idioma: inglés
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• Resumen

  • The purpose of this paper is to study categorifications of tensor products of finite-dimensional modules for the quantum group for ( ). The main categorification is obtained using certain Harish-Chandra bimodules for the complex Lie algebra ( ) . For the special case of simple modules we naturally deduce a categorification via modules over the cohomology ring of certain flag varieties. Further geometric categorifications and the relation to Steinberg varieties are discussed.We also give a categorical version of the quantised Schur¿Weyl duality and an interpretation of the (dual) canonical bases and the (dual) standard bases in terms of projective, tilting, standard and simple Harish-Chandra bimodules.