  We develop an elementary algebraic method to compute the center of the
principal block of a small quantum group associated with a complex semisimple
Lie algebra at a root of unity. The exemplary case of $\mathfrak{sl}_3$ is
computed explicitly, and further evidence of $\mathfrak{sl}_4$ is sketched.
This allows us to formulate the conjecture that, as a bigraded vector space,
the center of a regular block of the small quantum $\mathfrak{sl}_m$ at a root
of unity is isomorphic to Haiman's diagonal coinvariant algebra for the
symmetric group $S_{m}$.
