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

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.