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We utilise SUSY quiver gauge theories to compute properties of Slodowyslices; these are spaces transverse to the nilpotent orbits of a Lie algebra$\mathfrak g$. We analyse classes of quiver theories, with Classical gauge andflavour groups, whose Higgs branch Hilbert series are the intersections betweenSlodowy slices and the nilpotent cone $\mathcal S\cap \mathcal N$ of$\mathfrak{g}$. We calculate refined Hilbert series for Classical algebras upto rank $4$ (and $A_5$), and find descriptions of their representation matrixgenerators as algebraic varieties encoding the relations of the chiral ring. Wealso analyse a class of dual quiver theories, whose Coulomb branches areintersections $\mathcal S\cap \mathcal N$; such dual quiver theories exist forthe Slodowy slices of $A$ algebras, but are limited to a subset of the Slodowyslices of $BCD$ algebras. The analysis opens new questions about the extent of$3d$ mirror symmetry within the class of SCFTs known as $T_\sigma^\rho(G)$theories. We also give simple group theoretic formulae for the Hilbert seriesof Slodowy slices; these draw directly on the $SU(2)$ embedding into $G$ of theassociated nilpotent orbit, and the Hilbert series of the nilpotent cone.

Quiver Theories and Formulae for Slodowy Slices of Classical Algebras