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6-valent vertex in the glN web category and its categorification
Abstract
We define a 2π/3-rotationally invariant 6-valent vertex in the glN web category. When N = 4, 5, we provide a categorification of the 6-valent vertex using glN foams and decompose the hexagon web into a direct sum of indecomposables. A similar decomposition is conjectured for N ≥ 6.
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BibTeX
@misc{grlj20266valent,
title = {{6-valent vertex in the $\mathfrakgl_N$ web category and its categorification}},
author = {Jernej Grlj and Mikhail Khovanov and Haihan Wu and Melissa Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.21566},
eprint = {2608.21566},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.21566},
}
RIS
TY - UNPB
TI - 6-valent vertex in the gl_N web category and its categorification
AU - Jernej Grlj
AU - Mikhail Khovanov
AU - Haihan Wu
AU - Melissa Zhang
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2608.21566
UR - https://arxiv.org/abs/2608.21566
AB - We define a 2π/3-rotationally invariant 6-valent vertex in the gl_N web category. When N = 4, 5, we provide a categorification of the 6-valent vertex using gl_N foams and decompose the hexagon web into a direct sum of indecomposables. A similar decomposition is conjectured for N ≥ 6.
ER -