For affine type A bow diagrams, non-emptiness of the associated bow variety is equivalent to supersymmetry of the corresponding brane diagram, which can be checked by a finite set of inequalities.
Of conical symplectic resolutions quantizations of conical symplectic resolutions ii: category o and symplectic duality
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Supersymmetry for brane diagrams and bow varieties
For affine type A bow diagrams, non-emptiness of the associated bow variety is equivalent to supersymmetry of the corresponding brane diagram, which can be checked by a finite set of inequalities.