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By Igor Frenkel, Mikhail Khovanov, Catharina Stroppel

The aim of this paper is to review categorifications of tensor items of finite-dimensional modules for the quantum staff for sl2. the most categorification is acquired utilizing sure Harish-Chandra bimodules for the advanced Lie algebra gln. For the specific case of easy modules we evidently deduce a categorification through modules over the cohomology ring of convinced flag forms. additional geometric categorifications and the relation to Steinberg types are discussed.We additionally provide a specific model of the quantised Schur-Weyl duality and an interpretation of the (dual) canonical bases and the (dual) regular bases when it comes to projective, tilting, commonplace and easy Harish-Chandra bimodules.

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Chari and A. Pressley. A Guide to Quantum Groups. Cambridge Univ. Press, 1994. [CG97] N. Chriss and V. Ginzburg. Representation Theory and Complex Geometry. Birkh¨ auser Boston, Boston, MA, 1997. [CR07] J. Chuang and R. Rouquier. Derived equivalences for symmetric groups and sl2 -categorification. arXiv: mathRT/0407205, to appear in Ann. , 2007. [CPS88] E. Cline, B. Parshall, and L. Scott. Finite-dimensional algebras and highest weight categories. J. Reine Angew. Math. 391 (1988), 85–99. [CI89] D.

C. Jantzen, and W. Soergel. Representations of quantum groups at a pth root of unity and of semisimple groups in characteristic p: independence of p. Ast´erisque 220 (1994). [AL03] H. H. Andersen and N. Lauritzen. Twisted Verma modules. In: Studies in Memory of Issai Schur, Progr. Math. 210, Birkh¨ auser, 2003, 1–26. [AS03] H. H. Andersen and C. Stroppel. Twisting functors on O. Represent. Theory 7 (2003), 681–699. [Bas68] H. Bass. Algebraic K-theory. W. A. Benjamin, New York, 1968. Vol. 12 (2006) [BGS96] Categorification of representations of quantum sl2 429 A.

This is clear from the formulas (34), hence kx1 = s. ˜ (x · λ) ֒→ T˜(x · λ) gives rise to an inclusion (d M ˜ (w0 x · λ)) s ֒→ The inclusion M 3 ˜ (x · λ) gives rise to a Hw0 T (x · λ). This implies kx = s. The surjection P˜ (x · λ) → M ˜ (w0 x · λ)) s . Hence L(w ˜ 0 x · λ) s occurs as a comsurjection Hw0 P˜ (x · λ) → (d M position factor in Hw P˜ (x · λ). This implies kx2 = s. The proposition follows. 2, to categorify the action of the Hecke algebra we restricted the (graded lifts) of the twisting functors H j to the category of modules with Verma flag, to force them to be exact.

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