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Conformally covariant boundary correlation functions with a quantum group

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] for explicitly solving 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 desired properties of the functions are guaranteed by natural representation theoretical properties of the vectors.