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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Extra resources for A categorification of finite-dimensional irreducible representations of quantum sl2 and their tensor products
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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.