Affine and cyclotomic webs

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.