Minimal presentations of gl_n-web categories
A minimal and nearly coefficient-free presentation of web categories for quantum gl_n.
Data
- Title: Minimal presentations of \(\mathfrak{{gl}}_n\)-web categories
- Authors: Genta Latifi and Daniel Tubbenhauer
- Status: to appear in J. Knot Theory Ramifications. Last update: Mon, 13 Apr 2026 03:49:29 EST
- arXiv: https://arxiv.org/abs/2112.12688
- Note: This is part of Genta Latifi's PhD thesis. Genta did the work; I mostly get the honour, and possibly the blame.
Abstract
In this paper we study categories of \(\mathfrak{gl}_n\)-webs which describe associated representation categories of the quantum group \(\mathrm{U}_q(\mathfrak{gl}_n)\). We give a minimal presentation of the category of \(\mathfrak{gl}_n\)-webs over a field with generic quantum parameters. We additionally describe an integral presentation which differs from others in the literature because it is “as coefficient-free as possible”.
What is the point?
Web categories give a diagrammatic language for quantum group representation theory. The fewer relations one needs, the better the language becomes: easier to teach, easier to compute with, and easier to compare across related settings. This paper pares the presentation down.
webs for quantum \(\mathfrak{gl}_n\).
minimal relations.
as coefficient-free as possible.
Pictures
Generators and a relation adapted to the integral setting.
