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Knot invariants and higher representation theory

The author constructs knot invariants categorifying the quantum knot variants for all representations of quantum groups. He shows that these invariants coincide with previous invariants defined by Khovanov for \mathfrak{sl}_2 and \mathfrak{sl}_3 and by Mazorchuk-Stroppel and Sussan for \mathfrak{sl}...

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Detalles Bibliográficos
Autor principal: Webster, Ben
Lenguaje:eng
Publicado: American Mathematical Society 2018
Materias:
Acceso en línea:http://cds.cern.ch/record/2312823
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author Webster, Ben
author_facet Webster, Ben
author_sort Webster, Ben
collection CERN
description The author constructs knot invariants categorifying the quantum knot variants for all representations of quantum groups. He shows that these invariants coincide with previous invariants defined by Khovanov for \mathfrak{sl}_2 and \mathfrak{sl}_3 and by Mazorchuk-Stroppel and Sussan for \mathfrak{sl}_n. The author's technique is to study 2-representations of 2-quantum groups (in the sense of Rouquier and Khovanov-Lauda) categorifying tensor products of irreducible representations. These are the representation categories of certain finite dimensional algebras with an explicit diagrammatic presentation, generalizing the cyclotomic quotient of the KLR algebra. When the Lie algebra under consideration is \mathfrak{sl}_n, the author shows that these categories agree with certain subcategories of parabolic category \mathcal{O} for \mathfrak{gl}_k.
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institution Organización Europea para la Investigación Nuclear
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publishDate 2018
publisher American Mathematical Society
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spelling cern-23128232021-04-21T18:51:31Zhttp://cds.cern.ch/record/2312823engWebster, BenKnot invariants and higher representation theoryMathematical Physics and MathematicsThe author constructs knot invariants categorifying the quantum knot variants for all representations of quantum groups. He shows that these invariants coincide with previous invariants defined by Khovanov for \mathfrak{sl}_2 and \mathfrak{sl}_3 and by Mazorchuk-Stroppel and Sussan for \mathfrak{sl}_n. The author's technique is to study 2-representations of 2-quantum groups (in the sense of Rouquier and Khovanov-Lauda) categorifying tensor products of irreducible representations. These are the representation categories of certain finite dimensional algebras with an explicit diagrammatic presentation, generalizing the cyclotomic quotient of the KLR algebra. When the Lie algebra under consideration is \mathfrak{sl}_n, the author shows that these categories agree with certain subcategories of parabolic category \mathcal{O} for \mathfrak{gl}_k.American Mathematical Societyoai:cds.cern.ch:23128232018
spellingShingle Mathematical Physics and Mathematics
Webster, Ben
Knot invariants and higher representation theory
title Knot invariants and higher representation theory
title_full Knot invariants and higher representation theory
title_fullStr Knot invariants and higher representation theory
title_full_unstemmed Knot invariants and higher representation theory
title_short Knot invariants and higher representation theory
title_sort knot invariants and higher representation theory
topic Mathematical Physics and Mathematics
url http://cds.cern.ch/record/2312823
work_keys_str_mv AT websterben knotinvariantsandhigherrepresentationtheory