Conformal blocks, q-combinatorics, and quantum group symmetry
Annales de l’Institut Henri Poincaré D, Tome 6 (2019) no. 3, pp. 449-487.
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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 𝔰𝔩 2 . The construction both highlights the representation theoretic origin of conformal block functions and explains the appearance of q-combinatorial formulas.

Accepté le :
Publié le :
DOI : 10.4171/aihpd/88
Classification : 81-XX, 05-XX, 16-XX, 60-XX
Mots-clés : Conformal blocks, conformal field theory (CFT), Dyck tilings, multiple SLEs, quantum group representations, $q$-combinatorics 
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     title = {Conformal blocks, $q$-combinatorics, and quantum group symmetry},
     journal = {Annales de l{\textquoteright}Institut Henri Poincar\'e D},
     pages = {449--487},
     volume = {6},
     number = {3},
     year = {2019},
     doi = {10.4171/aihpd/88},
     mrnumber = {4002673},
     zbl = {1432.81054},
     language = {en},
     url = {http://archive.numdam.org/articles/10.4171/aihpd/88/}
}
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Karrila, Alex; Kytölä, Kalle; Peltola, Eveliina. Conformal blocks, $q$-combinatorics, and quantum group symmetry. Annales de l’Institut Henri Poincaré D, Tome 6 (2019) no. 3, pp. 449-487. doi : 10.4171/aihpd/88. http://archive.numdam.org/articles/10.4171/aihpd/88/

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