2017/09/30 by Alex Karrila, Kalle Kytölä, Eveliina Peltola
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics #Conformal field theory #Conformal map #Conformal symmetry #Geometry #Group (periodic table) #Mathematics #Partition (number theory) #Partition function (quantum field theory) #Physics #Pure mathematics #Quantum mechanics #Random Matrices and Applications #Representation theory #math-ph #math.MP #msc:05B20 #msc:16T05 #msc:60D05 #msc:81T40.
paper · pdf · doi:10.4171/aihpd/88
published as Ann. Inst. Henri Poincaré D, 6(3):449-487, 2019 · 24 pages, 7 figures. v3: minor improvements. Accepted for publication in Annales de l'Institut Henri Poincaré D
arxiv created 2018/11/05 · openalex publication_date 2019/04/09 · arxiv updated 2020/10/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 sl2 . The construction both highlights the representation theoretic origin of conformal block functions and explains the appearance of q -combinatorial formulas.