Zero-form and one-form symmetries of the ABJ and related theories

The zero-form and one-form global symmetries of the Aharony-Bergman-Jafferis (ABJ) related theories, with at least $\mathcal{N}=6$ supersymmetry in three dimensions, are examined detail. Starting from well-known dualities between theories orthogonal symplectic gauge groups those unitary groups, we their or subgroups obtain new dualities. One side latter involves special other groups; there is a discrete quotient on one both sides duality. We study refined superconformal indices such map across dualities, particular attention to part. As generalisation, also find duality circular quiver alternating three-dimensional $\mathcal{N}=4$ (Kronheimer-Nakajima) whose Higgs Coulomb branch describes an instanton singular orbifold.