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 -deformation of the Lie algebra . We show that the desired properties of the functions are guaranteed by natural representation-theoretical properties of the vectors.
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Kalle Kytölä, Eveliina Peltola, Conformally covariant boundary correlation functions with a quantum group. J. Eur. Math. Soc. 22 (2020), no. 1, pp. 55–118DOI 10.4171/JEMS/917