Cauchy–Szegö commutators on weighted Morrey spaces

In the setting of quaternionic Heisenberg group $$\mathcal H^{n-1}$$, we characterize the boundedness and compactness of commutator $$[b,\mathcal {C}]$$ for the Cauchy–Szegö operator $$\mathcal {C}$$ on the weighted Morrey space $$L_w^{p,\,\kappa }(\mathcal H^{n-1})$$ with $$p\in (1, \infty )$$, $$\kappa \in (0, 1)$$, and $$w\in A_p(\mathcal H^{n-1})$$. More precisely, we prove that $$[b,\mathcal {C}]$$ is bounded on $$L_w^{p,\,\kappa }(\mathcal H^{n-1})$$ if and only if $$b\in {\rm BMO}(\mathcal H^{n-1})$$. And $$[b,\mathcal {C}]$$ is compact on $$L_w^{p,\,\kappa }(\mathcal H^{n-1})$$ if and only if $$b\in {\rm VMO}(\mathcal H^{n-1})$$.