  In this article, we find a $q$-analogue for Fomin's formulas. The original
Fomin's formulas relate determinants of random walk excursion kernels to
loop-erased random walk partition functions, and our formulas analogously
relate conformal block functions of conformal field theories to pure partition
functions of multiple SLE random curves. We also provide a construction of the
conformal block functions by a method based on a quantum group, the
$q$-deformation of $\mathfrak{sl}_2$. The construction both highlights the
representation theoretic origin of conformal block functions and explains the
appearance of $q$-combinatorial formulas.
