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Knot Invariants and Higher Representation Theory by Ben Webster; American Mathematical Society is a nonfiction available to read on EtoBox.

What is Knot Invariants and Higher Representation Theory about?

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 $\mathfrak{gl}\_k$.

Who reads Knot Invariants and Higher Representation Theory?

Author

Ben Webster; American Mathematical Society

Publisher

American Mathematical Society

Published

2018

Language

EN

ISBN

9781470442064

Category

nonfiction

Subjects

Mathematics, Stem