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A Categorification of Finite-dimensional Irreducible Representations of Quantum $${\Mathfrak{sl}\_2}$$ and Their Tensor Products by Igor Frenkel, Mikhail Khovanov, Catharina Stroppel is a nonfiction available to read on EtoBox.

What is A Categorification of Finite-dimensional Irreducible Representations of Quantum $${\Mathfrak{sl}\_2}$$ and Their Tensor Products about?

The purpose of this paper is to study categorifications of tensor products of finite-dimensional modules for the quantum group for sl2. The main categorification is obtained using certain Harish-Chandra bimodules for the complex Lie algebra gln. 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.

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Author

Igor Frenkel, Mikhail Khovanov, Catharina Stroppel

Publisher

SP Birkhäuser Verlag Basel; Springer-Verlag; Birkhauser Verlag; Springer Science and Business Media LLC (ISSN 1022-1824)

Published

2007

Language

EN

Category

nonfiction

Subjects

Science, Mathematics, Physics