  In this note, we extend the striking connections between quantum integrable
systems and conformal blocks recently found in http://arxiv.org/abs/1602.01858
in several directions. First, we explicitly demonstrate that the action of
quartic conformal Casimir operator on general d-dimensional scalar conformal
blocks, can be expressed in terms of certain combinations of commuting
integrals of motions of the two particle hyperbolic BC2 Calogero-Sutherland
system. The permutation and reflection properties of the underlying Dunkl
operators play crucial roles in establishing such a connection. Next, we show
that the scalar superconformal blocks in SCFTs with four and eight supercharges
and suitable chirality constraints can also be identified with the
eigenfunctions of the same Calogero-Sutherland system, this demonstrates the
universality of such a connection. Finally, we observe that the so-called
"seed" conformal blocks for constructing four point functions for operators
with arbitrary space-time spins in four dimensional CFTs can also be linearly
expanded in terms of Calogero-Sutherland eigenfunctions.
