By Igor Frenkel, Mikhail Khovanov, Catharina Stroppel
The aim of this paper is to check categorifications of tensor items of finite-dimensional modules for the quantum team for sl2. the most categorification is got utilizing definite Harish-Chandra bimodules for the complicated Lie algebra gln. For the distinctive case of easy modules we evidently deduce a categorification through modules over the cohomology ring of convinced flag kinds. additional geometric categorifications and the relation to Steinberg types are discussed.We additionally provide a express model of the quantised Schur-Weyl duality and an interpretation of the (dual) canonical bases and the (dual) normal bases when it comes to projective, tilting, commonplace and straightforward Harish-Chandra bimodules.
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Extra info for A categorification of finite-dimensional irreducible representations of quantum sl2 and their tensor products
However, we have the following stronger result: 418 I. Frenkel, M. Khovanov and C. Stroppel Sel. , New ser. 1. There is an equivalence of categories n n Ai−ρ → F : C i -gmod i=0 i=0 which intertwines the functors Ei , Fi , and Ki with the functors i,i+1 Ei = Resi,i+1 ⊗C i −n + i + 1 , i+1 C i,i−1 Fi = Resi,i−1 ⊗C i −i + 1 , i−1 C Ki = 2i − n . be the unique (up to isomorphism) indecomposable projecProof. Let P ∈ A−ρ i tive module such that its head is concentrated in degree zero. Then we have an isomorphism of graded algebras EndA−ρ (P ) ∼ = EndAi (P (w0 · ωi )) ∼ = C i .
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