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

Andrew Mathas, Daniel Tubbenhauer

Published 2022-01-06, updated 2022-04-13Version 2

This paper constructs homogeneous affine sandwich cellular bases of weighted KLRW algebras in types $B_{\mathbb{Z}_{\geq 0}}$, $A^{(2)}_{2\cdot e}$, $D^{(2)}_{e+1}$. 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 (finite dimensional) KLR algebras.