Conformal blocks, $q$-combinatorics, and quantum group symmetry
Mathematical Physics
2020-10-27 v3 math.MP
Abstract
In this article, we find a -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 -deformation of . The construction both highlights the representation theoretic origin of conformal block functions and explains the appearance of -combinatorial formulas.
Cite
@article{arxiv.1709.00249,
title = {Conformal blocks, $q$-combinatorics, and quantum group symmetry},
author = {Alex Karrila and Kalle Kytölä and Eveliina Peltola},
journal= {arXiv preprint arXiv:1709.00249},
year = {2020}
}
Comments
24 pages, 7 figures. v3: minor improvements. Accepted for publication in Annales de l'Institut Henri Poincar\'e D