Knot Invariants and Higher Representation Theory - Couverture souple

Webster, Ben

Couverture souple

ISBN 10 : 1470426501 ISBN 13 : 9781470426507

Editeur : American Mathematical Society, 2018

Synopsis

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 $\mathfrak{gl}_k$.

A propos du livre

À propos de l'auteur

Ben Webster, University of Virginia, Charlottesville, VA.

Détails de l'édition

• Éditeur: American Mathematical Society
• Date d'édition: 2018
• Langue: anglais
• ISBN 10: 1470426501
• ISBN 13: 9781470426507
• Reliure: Broché
• Nombre de pages: 133
• Coordonnées du fabricant: non disponible
• Personne responsable: non disponible