Download A categorification of finite-dimensional irreducible by Igor Frenkel, Mikhail Khovanov, Catharina Stroppel PDF

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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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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