English

Affine and cyclotomic webs

Representation Theory 2026-01-08 v3 Quantum Algebra

Abstract

Generalizing the polynomial web category, we introduce a diagrammatic k\Bbbk-linear monoidal category, the affine web category, for any commutative ring k\Bbbk. 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 WW-algebras are established, leading to a diagrammatic presentation of idempotent subalgebras of WW-Schur algebras introduced by Brundan-Kleshchev. The affine web category will be used as a basic building block of another k\Bbbk-linear monoidal category, the affine Schur category, formulated in a sequel.

Keywords

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

R2 v1 2026-06-28T17:11:26.215Z