ENGLISH

Knot Invariants and Higher Representation Theory

By Ben Webster

Book information

Publisher
American Mathematical Society
Year
2018
ISBN
9781470442064, 9781470426507
LCC
QA612.2 .W437 2017
Language
english
Format
PDF
Filesize
1 MB (1382320 bytes)
Series
Memoirs of the American Mathematical Society
Edition
1
Pages
154\154
Time added
2023-08-20 03:13:36
Knot theory.

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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