  We consider the systems of diffusion-orthogonal polynomials, defined in the
work [1] of D. Bakry, S. Orevkov and M. Zani and (particularly) explain why
these systems with boundary of maximal possible degree should always come from
the group, generated by reflections. Our proof works for the dimensions $2$ (on
which this phenomena was discovered) and $3$, and fails in the dimensions $4$
and higher, leaving the possibility of existence of diffusion-orthogonal
systems related to the Einstein metrics.
  The methods of our proof are algebraic / complex analytic in nature and based
mainly on the consideration of the double covering of $\mathbb{C}^d$, branched
in the boundary divisor.
  Author wants to thank Stepan Orevkov, Misha Verbitsky and Dmitry Korb for
useful discussions.
