TY - JOUR
T1 - Conformal blocks, q-combinatorics, and quantum group symmetry
AU - Karrila, Alex
AU - Kytölä, Kalle
AU - Peltola, Eveliina
PY - 2019/4/9
Y1 - 2019/4/9
N2 - 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 sl2. The construction both highlights the representation theoretic origin of conformal block functions and explains the appearance of q-combinatorial formulas.
AB - 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 sl2. The construction both highlights the representation theoretic origin of conformal block functions and explains the appearance of q-combinatorial formulas.
UR - https://www.ems-ph.org/journals/of_list.php?jrn=aihpd
UR - https://arxiv.org/abs/1709.00249
U2 - 10.4171/AIHPD/88
DO - 10.4171/AIHPD/88
M3 - Article
VL - 6
SP - 449
EP - 487
JO - Annales de l’Institut Henri Poincaré D
JF - Annales de l’Institut Henri Poincaré D
SN - 2308-5827
IS - 3
ER -