Conformal blocks, -combinatorics, and quantum group symmetry

  • Alex Karrila

    Aalto University, Finland
  • Kalle Kytölä

    Aalto University, Finland
  • Eveliina Peltola

    Université de Genève, Switzerland
Conformal blocks, $q$-combinatorics, and quantum group symmetry cover

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Abstract

In this article, we find a -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 -deformation of . The construction both highlights the representation theoretic origin of conformal block functions and explains the appearance of -combinatorial formulas.

Cite this article

Alex Karrila, Kalle Kytölä, Eveliina Peltola, Conformal blocks, -combinatorics, and quantum group symmetry. Ann. Inst. Henri Poincaré Comb. Phys. Interact. 6 (2019), no. 3, pp. 449–487

DOI 10.4171/AIHPD/88