  BPS algebras are the symmetries of a wide class of brane-inspired models.
They are closely related to Yangians -- the peculiar and somewhat sophisticated
limit of DIM algebras. Still they possess some simple and explicit
representations. We explain here that for $Y(\widehat{\mathfrak{gl}}_r)$ these
representations are related to Uglov polynomials, whose families are also
labeled by natural $r$. They arise in the limit $\hbar\longrightarrow 0$ from
Macdonald polynomials, and generalize the well-known Jack polynomials
($\beta$-deformation of Schur functions), associated with $r=1$. For $r=2$ they
approximate Macdonald polynomials with the accuracy $O(\hbar^2)$, so that they
are eigenfunctions of {\it two} immediately available commuting operators,
arising from the $\hbar$-expansion of the first Macdonald Hamiltonian. These
operators have a clear structure, which is easily generalizable, -- what
provides a technically simple way to build an explicit representation of
Yangian $Y(\widehat{\mathfrak{gl}}_2)$, where $U^{(2)}$ are associated with the
states $|\lambda\rangle$, parametrized by chess-colored Young diagrams. An
interesting feature of this representation is that the odd time-variables
$p_{2n+1}$ can be expressed through mutually commuting operators from Yangian,
however even time-variables $p_{2n}$ are inexpressible. Implications to higher
$r$ become now straightforward, yet we describe them only in a sketchy way.
