Abstract
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.