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 $A_{s-1}^{(1)}$, $C_s^{(1)}$, $A_{2s}^{(2)}$, $D_s^{(2)}$. We derive a unified dimension formula for the bi-weight spaces for cyclotomic quiver Hecke-Clifford superalgebras of types $A_{s-1}^{(1)}$, $C_s^{(1)}$, $A_{2s}^{(2)}$, $D_s^{(2)}$. We introduce the notion of generalized graded cellular superalgebra. We prove a large class of cyclotomic quiver Hecke-Clifford superalgebras of types $A_{s-1}^{(1)}$, $C_s^{(1)}$, $A_{2s}^{(2)}$, $D_s^{(2)}$ is generalized graded cellular. By taking idempotent truncation, this recovers the known graded cellualr results for cyclotomic quiver Hecke algebras of types $A_{s-1}^{(1)}$, $C_s^{(1)}$.