Knot Invariants and Higher Representation Theory
Author | : Benjamin Thomas Webster |
Publisher | : |
Total Pages | : 141 |
Release | : 2017 |
ISBN-10 | : 147044206X |
ISBN-13 | : 9781470442064 |
Rating | : 4/5 (6X Downloads) |
Book excerpt: 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 presen.