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Pure Partition Functions of Multiple SLEs

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Abstract

Multiple Schramm–Loewner Evolutions (SLE) are conformally invariant random processes of several curves, whose construction by growth processes relies on partition functions—Möbius covariant solutions to a system of second order partial differential equations. In this article, we use a quantum group technique to construct a distinguished basis of solutions, which conjecturally correspond to the extremal points of the convex set of probability measures of multiple SLEs.

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Authors and Affiliations

  1. Department of Mathematics and Systems Analysis, Aalto University, P.O. Box 11100, 00076, Espoo, Finland

    Kalle Kytölä

  2. Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68, 00014, Helsinki, Finland

    Eveliina Peltola

Authors
  1. Kalle Kytölä
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  2. Eveliina Peltola
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Correspondence to Kalle Kytölä.

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Communicated by A. Borodin

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Kytölä, K., Peltola, E. Pure Partition Functions of Multiple SLEs. Commun. Math. Phys. 346, 237–292 (2016). https://doi.org/10.1007/s00220-016-2655-2

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  • DOI: https://doi.org/10.1007/s00220-016-2655-2

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