Knot Invariants and Higher Representation Theory

Released on by Ben Webster
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  • Knot Invariants and Higher Representation Theory Book Detail

  • Author : Ben Webster
  • Release Date : 2018-01-16
  • Publisher : American Mathematical Soc.
  • Genre : Mathematics
  • Pages : 154
  • ISBN 13 : 1470426501
  • File Size : 42,42 MB
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Knot Invariants and Higher Representation Theory by Ben Webster PDF Summary

Book 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 sl and sl and by Mazorchuk-Stroppel and Sussan for sl . 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 sl , the author shows that these categories agree with certain subcategories of parabolic category for gl .

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