On the generalized graded cellular bases for cyclotomic quiver Hecke-Clifford superalgebras

In this paper, we construct semisimple deformations for cyclotomic quiver Hecke-Clifford superalgebras of types $A^{(1)}_{s-1}$, $C^{(1)}_{s}$, $A^{(2)}_{2s}$, $D^{(2)}_{s}$. We derive a unified dimension formula for the bi-weight spaces for cyclotomic quiver Hecke-Clifford superalgebras of types $A^{(1)}_{s-1}$, $C^{(1)}_{s}$, $A^{(2)}_{2s}$, $D^{(2)}_{s}$. We introduce the notion of generalized graded cellular superalgebra. We prove a large class of cyclotomic quiver Hecke-Clifford superalgebras of types $A^{(1)}_{s-1}$, $C^{(1)}_{s}$, $A^{(2)}_{2s}$, $D^{(2)}_{s}$ is generalized graded cellular. By taking idempotent truncation, this recovers the known graded cellualr results for cyclotomic quiver Hecke algebras of types $A^{(1)}_{s-1}$, $C^{(1)}_{s}$.