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 team for sl2. the most categorification is received utilizing yes Harish-Chandra bimodules for the advanced Lie algebra gln. For the detailed case of straightforward modules we obviously deduce a categorification through modules over the cohomology ring of convinced flag kinds. additional geometric categorifications and the relation to Steinberg forms are discussed.We additionally supply 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, normal and easy Harish-Chandra bimodules.
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Additional resources for A categorification of finite-dimensional irreducible representations of quantum sl2 and their tensor products
Then we proceed to the geometric categorification of general tensor products using certain algebras of functions which generalise the cohomology rings and point towards the Borel–Moore homology of generalised Steinberg varieties. We conclude this section by formulating open problems related to the geometric categorification. 1. From algebraic to geometric categorification The categorification of simple Uq (sl2 )-modules we propose gives rise to a categorification of simple U(sl2 )-modules by forgetting the grading.
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