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Knot Invariants and Higher Representation Theory (Memoirs of the American Mathematical Society)

Algebra

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Description

About the Author Ben Webster, University of Virginia, Charlottesville, VA. Product 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 $\mathfrak{gl}_k$.

Product Specifications

Format: Paperback
ASIN: 1470426501
Category: Books > Subjects > Science, Nature & Maths > Mathematics > Algebra
Domain: Amazon UK
Release Date: 28 February 2018
Listed Since: 18 August 2017

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Knot Invariants and Higher Representation Theory (Memoirs of the American Mathematical Society)

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