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- W1627626561 abstract "The purpose of this paper is to study categorifications of tensor products of finite-dimensional modules for the quantum group for $${mathfrak{sl}_2}$$ . The main categorification is obtained using certain Harish-Chandra bimodules for the complex Lie algebra $${mathfrak{gl}_n}$$ . For the special case of simple modules we naturally deduce a categorification via modules over the cohomology ring of certain flag varieties. Further geometric categorifications and the relation to Steinberg varieties are discussed.We also give a categorical version of the quantised Schur–Weyl duality and an interpretation of the (dual) canonical bases and the (dual) standard bases in terms of projective, tilting, standard and simple Harish-Chandra bimodules." @default.
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- W1627626561 date "2007-03-13" @default.
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- W1627626561 title "A categorification of finite-dimensional irreducible representations of quantum $${mathfrak{sl}_2}$$ and their tensor products" @default.
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- W1627626561 doi "https://doi.org/10.1007/s00029-007-0031-y" @default.
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