Work

6-valent vertex in the $\mathfrak{gl}_N$ web category and its categorification

Year: 2026

Type: preprint

Abstract: We define a $2π/3$-rotationally invariant 6-valent vertex in the $\mathfrak{gl}_N$ web category. When $N = 4, 5$, we provide a categorification of the 6-valent vertex using $\mathfrak{gl}_N$ foams and decompose the hexagon web into a direct sum of indecomposables. A similar decomposition is conjectured for $N \geq 6$.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2608.21566

Authors: Grlj, Jernej, Khovanov, Mikhail, Wu, Haihan, Zhang, Melissa

Institutions: Johns Hopkins University, University of Southern California, University of California, Davis

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7204159765

Cites: 7

Cited by:

Related to: 10