## Data

• Title: Minimal presentations of $$\mathfrak{gl}_n$$-web categories
• Authors: Genta Latifi and Daniel Tubbenhauer
• Status: preprint. Last update: Thu, 23 Dec 2021 16:32:53 UTC
In this paper we study categories of $$\mathfrak{gl}_n$$-webs which describe associated representation categories of the quantum group $$\text{U}_{q}(\mathfrak{gl}_n)$$. 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”.
This paper studies symmetric and exterior categories of $$\mathfrak{gl}_n$$-webs (strictly speaking only symmetric one, but the arguments work mutatis mutandis in the exterior case as well), and we discuss minimal and integral presentations of these categories.