A categorification of finite-dimensional irreducible representations of quantum({mathfrak{sl}_2})and their tensor products
✍ Scribed by Igor Frenkel; Mikhail Khovanov; Catharina Stroppel
- Publisher
- SP Birkhäuser Verlag Basel
- Year
- 2007
- Tongue
- English
- Weight
- 495 KB
- Volume
- 12
- Category
- Article
- ISSN
- 1022-1824
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✦ Synopsis
The purpose of this paper is to study categorifications of tensor products of finite-dimensional modules for the quantum group for sl2. The main categorification is obtained using certain Harish-Chandra bimodules for the complex Lie algebra gln. 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.