Leading term strandings for webs
Abstract
A web is a plane graph encoding an invariant vector in a tensor product of fundamental representations of a quantum group. A stranding of an sln web is a system of colored oriented curves recording one monomial of the vector it encodes. This article focuses on identifying and constructing leading term strandings, those recording the leading term of a web's vector with respect to a lexicographic order on monomials. We show that every open strand of a leading term stranding is clockwise, so the boundary data of such a stranding is recorded by a row-strict tableau. From a row-strict tableau, we construct a web with a prescribed leading term, and the resulting webs form a web basis. This non recursive construction recovers Fontaine's bases and produces others. For sl3 webs with no flat vertices, we identify a leading term stranding using the depths of the faces of the web. Finally, we ask whether any two strandings of a web are connected by a sequence of local moves called strand reversals. We answer this question affirmatively for sl3, extending a known result for closed webs to webs with boundary; in particular, a leading term stranding of any sl3 web is always reachable from an arbitrary stranding.
Related
- Brauer webs of finite and affine type
- Chromatic symmetric functions for annular webs
- Equilibrium webs and stability for arbitrary families of endomorphisms of projective spaces
- Holomorphy of the curvature of planar webs along an invariant curve and applications to the flatness of certain webs on ℙ2ℂ
- PGL2 webs at roots of unity
BibTeX
@misc{bo2026leading,
title = {{Leading term strandings for webs}},
author = {Michael Bo and Madelyn Burns and Junyang Chen and Blaise Marsho and Jacob Martin and Jade Mawn and Bella Mohren and Heather M. Russell and Caitlin Sales and Lance Wong},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.27425},
eprint = {2608.27425},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.27425},
}
RIS
TY - UNPB
TI - Leading term strandings for webs
AU - Michael Bo
AU - Madelyn Burns
AU - Junyang Chen
AU - Blaise Marsho
AU - Jacob Martin
AU - Jade Mawn
AU - Bella Mohren
AU - Heather M. Russell
AU - Caitlin Sales
AU - Lance Wong
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2608.27425
UR - https://arxiv.org/abs/2608.27425
AB - A web is a plane graph encoding an invariant vector in a tensor product of fundamental representations of a quantum group. A stranding of an sl_n web is a system of colored oriented curves recording one monomial of the vector it encodes. This article focuses on identifying and constructing leading term strandings, those recording the leading term of a web's vector with respect to a lexicographic order on monomials. We show that every open strand of a leading term stranding is clockwise, so the boundary data of such a stranding is recorded by a row-strict tableau. From a row-strict tableau, we construct a web with a prescribed leading term, and the resulting webs form a web basis. This non recursive construction recovers Fontaine's bases and produces others. For sl_3 webs with no flat vertices, we identify a leading term stranding using the depths of the faces of the web. Finally, we ask whether any two strandings of a web are connected by a sequence of local moves called strand reversals. We answer this question affirmatively for sl_3, extending a known result for closed webs to webs with boundary; in particular, a leading term stranding of any sl_3 web is always reachable from an arbitrary stranding.
ER -