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This article pertains to the classification of multiple Schramm-Loewnerevolutions (SLE). We construct the pure partition functions of multipleSLE$(\kappa)$ with $\kappa \in (0,4]$ and relate them to certain extremalmultiple SLE measures, thus verifying a conjecture from [BBK05, KP16]. We provethat the two approaches to construct multiple SLEs - the global,configurational construction of [KL07, Law09a] and the local, growth processconstruction of [BBK05, Dub07, Gra07, KP16] - agree. The pure partitionfunctions are closely related to crossing probabilities in critical statisticalmechanics models. With explicit formulas in the special case of $\kappa = 4$,we show that these functions give the connection probabilities for the levellines of the Gaussian free field (GFF) with alternating boundary data. We alsoshow that certain functions, known as conformal blocks, give rise to multipleSLE(4) that can be naturally coupled with the GFF with appropriate boundarydata.

Global and Local Multiple SLEs for $\kappa \leq 4$ and Connection Probabilities for Level Lines of GFF