Cellularity for weighted KLRW algebras of types $B$, $A^{(2)}$, $D^{(2)}$

TL;DR

This paper develops cellular bases for weighted KLRW algebras of types B, A^{(2)}, D^{(2)}, leading to new bases and cellularity results for related KLR algebras, both finite and infinite dimensional.

Contribution

It introduces homogeneous affine sandwich cellular bases for weighted KLRW algebras in specific types, extending to KLR algebras and their quotients.

Findings

Constructed homogeneous affine sandwich cellular bases for weighted KLRW algebras.

Derived cellularity results for finite dimensional quotients.

Extended bases and cellularity to KLR algebras, both finite and infinite dimensional.

Abstract

This paper constructs homogeneous affine sandwich cellular bases of weighted KLRW algebras in types $B$, $A^{(2)}$, $D^{(2)}$. Our construction immediately gives homogeneous sandwich cellular bases for the finite dimensional quotients of these algebras. Since weighted KLRW algebras generalize KLR algebras, we also obtain bases and cellularity results for the (infinite and finite dimensional) KLR algebras.