A generalization of adjoint crystals for the quantized affine algebras of type $A\text{sb}n\text{sp}(1)$, $C\text{sb}n\text{sp}(1)$ and $D\text{sb}n+1\text{sp}(2)$

We propose to generalize Benkart-Frenkel-Kang-Lee’s adjoint crystals and describe their crystal structure for type $A\text{sb}n\text{sp}(1)$, $C\text{sb}n\text{sp}(1)$ and $D\text{sb}n+1\text{sp}(2)$.