Affine and cyclotomic webs
Representation Theory
2026-01-08 v3 Quantum Algebra
Abstract
Generalizing the polynomial web category, we introduce a diagrammatic -linear monoidal category, the affine web category, for any commutative ring . Integral bases consisting of elementary diagrams are obtained for the affine web category and its cyclotomic quotient categories. Connections between cyclotomic web categories and finite -algebras are established, leading to a diagrammatic presentation of idempotent subalgebras of -Schur algebras introduced by Brundan-Kleshchev. The affine web category will be used as a basic building block of another -linear monoidal category, the affine Schur category, formulated in a sequel.
Cite
@article{arxiv.2406.13172,
title = {Affine and cyclotomic webs},
author = {Linliang Song and Weiqiang Wang},
journal= {arXiv preprint arXiv:2406.13172},
year = {2026}
}
Comments
V3, minor corrections and updates, to appear in JLMS