Conformal blocks, q-combinatorics, and quantum group symmetry

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7 Citations (Scopus)


In this article, we find a q-analogue for Fomin’s formulas. The original Fomin’s formulas relate determinants of random walk excursion kernels to loop-erased random walk partition functions, and our formulas analogously relate conformal block functions of conformal field theories to pure partition functions of multiple SLE random curves. We also provide a construction of the conformal block functions by a method based on a quantum group, the q-deformation of sl2. The construction both highlights the representation theoretic origin of conformal block functions and explains the appearance of q-combinatorial formulas.
Original languageEnglish
Pages (from-to)449-487
Number of pages39
JournalAnnales de l’Institut Henri Poincaré D
Issue number3
Publication statusPublished - 9 Apr 2019
MoE publication typeA1 Journal article-refereed


  • Conformal blocks
  • Conformal field theory (CFT)
  • Dyck tilings
  • Multiple SLEs
  • Q-combinatorics
  • Quantum group representations


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