We give an explicit formula for the Higgs and Coulomb branch Hilbert series
for the class of 3d N = 4 superconformal gauge theories T
σ
ρ
(G) corresponding to a set of
D3 branes ending on NS5 and D5-branes, with or without O3 planes. Here G is a classical
group, σ is a partition of G and ρ a partition of the dual group G∨. In deriving such a
formula we make use of the recently discovered formula for the Hilbert series of the quantum
Coulomb branch of N = 4 superconformal theories. The result can be expressed in terms
of a generalization of a class of symmetric functions, the Hall-Littlewood polynomials,
and can be interpreted in mathematical language in terms of localization. We mainly
consider the case G = SU(N) but some interesting results are also given for orthogonal
and symplectic groups