TY - JOUR
T1 - Conformally covariant boundary correlation functions with a quantum group
AU - Kytölä, Kalle
AU - Peltola, Eveliina
N1 - Funding Information:
We thank Michel Bauer, Denis Bernard, Dmitry Chelkak, Steven Flores, Philippe Di Francesco, Azat Gainutdinov, Christian Hagendorf, Cl?ment Hongler, Konstantin Izyurov, Niko Jokela, Matti J?rvinen, Peter Kleban, Hubert Saleur, and Jacob Simmons for interesting discussions, useful comments, and suggested improvements. We also thank the anonymous referees for useful suggestions. This work was supported by the Academy of Finland. E.P. was supported by the Finnish National Doctoral Programme in Mathematics and its Applications and Vilho, Yrj? and Kalle V?is?l? Foundation. The work was carried out while E.P. was affiliated with the University of Helsinki.
Funding Information:
This work was supported by the Academy of Finland. E.P. was supported by the Finnish National Doctoral Programme in Mathematics and its Applications and Vilho, Yrjö and Kalle Väisälä Foundation. The work was carried out while E.P. was affiliated with the University of Helsinki.
Publisher Copyright:
© European Mathematical Society 2020.
PY - 2020
Y1 - 2020
N2 - Particular boundary correlation functions of conformal field theory are needed to answer some questions related to random conformally invariant curves known as Schramm-Loewner evolutions (SLE). In this article, we introduce a correspondence and establish its fundamental properties, which are used in the companion articles [JJK16, KP16] to explicitly solve two such problems. The correspondence associates Coulomb gas type integrals to vectors in a tensor product representation of a quantum group, a q-deformation of the Lie algebra sl2. We show that the desired properties of the functions are guaranteed by natural representation-theoretical properties of the vectors.
AB - Particular boundary correlation functions of conformal field theory are needed to answer some questions related to random conformally invariant curves known as Schramm-Loewner evolutions (SLE). In this article, we introduce a correspondence and establish its fundamental properties, which are used in the companion articles [JJK16, KP16] to explicitly solve two such problems. The correspondence associates Coulomb gas type integrals to vectors in a tensor product representation of a quantum group, a q-deformation of the Lie algebra sl2. We show that the desired properties of the functions are guaranteed by natural representation-theoretical properties of the vectors.
KW - Conformal field theory
KW - Partial differential equations
KW - Quantum group
KW - Schramm-Loewner evolution
UR - http://www.scopus.com/inward/record.url?scp=85077336288&partnerID=8YFLogxK
UR - http://arxiv.org/abs/1408.1384
UR - http://www.ems-ph.org/journals/forthcoming.php?jrn=jems
U2 - 10.4171/JEMS/917
DO - 10.4171/JEMS/917
M3 - Article
AN - SCOPUS:85077336288
SN - 1435-9855
VL - 22
SP - 55
EP - 118
JO - Journal of the European Mathematical Society
JF - Journal of the European Mathematical Society
IS - 1
ER -