Conformal blocks, q-combinatorics, and quantum group symmetry

Alex Karrila; Kalle Kytölä; Eveliina Peltola

doi:10.4171/AIHPD/88

Conformal blocks, q-combinatorics, and quantum group symmetry

Alex Karrila, Kalle Kytölä, Eveliina Peltola

University of Geneva

Research output: Contribution to journal › Article › Scientific › peer-review

7 Citations (Scopus)

Abstract

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 language	English
Pages (from-to)	449-487
Number of pages	39
Journal	Annales de l’Institut Henri Poincaré D
Volume	6
Issue number	3
DOIs	https://doi.org/10.4171/AIHPD/88
Publication status	Published - 9 Apr 2019
MoE publication type	A1 Journal article-refereed

Keywords

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

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10.4171/AIHPD/88

https://arxiv.org/pdf/1709.00249

Cite this

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title = "Conformal blocks, q-combinatorics, and quantum group symmetry",

abstract = "In this article, we find a q-analogue for Fomin{\textquoteright}s formulas. The original Fomin{\textquoteright}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.",

keywords = "Conformal blocks, Conformal field theory (CFT), Dyck tilings, Multiple SLEs, Q-combinatorics, Quantum group representations",

author = "Alex Karrila and Kalle Kyt{\"o}l{\"a} and Eveliina Peltola",

note = "Funding Information: A. Karrila and K. Kyt{\"o}l{\"a} are supported by the Academy of Finland project “Algebraic structures and random geometry of stochastic lattice models.” A. Karrila is also supported by the Vilho, Yrj{\"o} and Kalle V{\"a}is{\"a}l{\"a} Foundation. E. Peltola is supported by the ERC AG COMPASP, the NCCR SwissMAP, and the Swiss NSF. Publisher Copyright: {\textcopyright} European Mathematical Society.",

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T1 - Conformal blocks, q-combinatorics, and quantum group symmetry

AU - Karrila, Alex

AU - Kytölä, Kalle

AU - Peltola, Eveliina

N1 - Funding Information: A. Karrila and K. Kytölä are supported by the Academy of Finland project “Algebraic structures and random geometry of stochastic lattice models.” A. Karrila is also supported by the Vilho, Yrjö and Kalle Väisälä Foundation. E. Peltola is supported by the ERC AG COMPASP, the NCCR SwissMAP, and the Swiss NSF. Publisher Copyright: © European Mathematical Society.

PY - 2019/4/9

Y1 - 2019/4/9

N2 - 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.

AB - 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.

KW - Conformal blocks

KW - Conformal field theory (CFT)

KW - Dyck tilings

KW - Multiple SLEs

KW - Q-combinatorics

KW - Quantum group representations

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UR - https://www.ems-ph.org/journals/of_list.php?jrn=aihpd

UR - https://arxiv.org/abs/1709.00249

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DO - 10.4171/AIHPD/88

M3 - Article

AN - SCOPUS:85073358717

SN - 2308-5827

VL - 6

SP - 449

EP - 487

JO - Annales de l’Institut Henri Poincaré D

JF - Annales de l’Institut Henri Poincaré D

IS - 3

ER -

Conformal blocks, q-combinatorics, and quantum group symmetry

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Keywords

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