Conformal blocks, -combinatorics, and quantum group symmetry
Alex Karrila, Kalle Kytölä, Eveliina Peltola
Source 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.
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