On matrix models and their q-deformations

Motivated by the BPS/CFT correspondence, we explore the similarities be- tween the classical beta -deformed Hermitean matrix model and the q-deformed matrix models associated to 3d N = 2 supersymmetric gauge theories on D(2)x(q)S(1) and Sb3 by matching parameters of the theories. The novel results that we obtain are the correlators for the models, together with an additional result in the classical case consisting of the W -algebra representation of the generating function. Furthermore, we also obtain surprisingly simple expressions for the expectation values of characters which generalize previously known results.