Orthosymplectic Quotient Quiver Subtraction II: Framed Quivers

The technique of $\textit{orthosymplectic quotient quiver subtraction}$ is introduced for framed orthosymplectic quivers. This involves subtracting an $\textit{orthosymplectic quotient quiver}$ from a framed orthosymplectic $3d\;\mathcal N=4$ quiver gauge theory which has the effect of gauging an $\mathrm{SO}(n)$ or $\mathrm{Sp}(n)$ subgroup of the IR Coulomb branch global symmetry with complete Higgsing. The orthosymplectic quotient quivers take the form of magnetic quivers for class $\mathcal S$ theories on cylinders with (twisted) maximal punctures of simply laced algebras, similar to the case of unitary quotient quiver subtraction. This gives a set of quotient quivers for all classical groups. Notably, quotient quiver subtraction for framed and unframed orthosymplectic quivers are different procedures.