[Formules algébriques closes explicites pour les fonctions à points d’Orlov-Scherbin]
Nous présentons une nouvelle formule explicite en termes de sommes sur les graphes pour les fonctions de corrélation à points des nombres de Hurwitz doubles pondérés formels généraux provenant des fonctions tau de Kadomtsev-Petviashvili de type hypergéométrique (également connues sous le nom de fonctions de partition d’Orlov-Scherbin). Nous utilisons notamment le changement de variables suggéré par la courbe spectrale associée, et notre formule s’avère être une expression polynomiale dans un certain petit ensemble de fonctions formelles définies sur la courbe spectrale.
We derive a new explicit formula in terms of sums over graphs for the -point correlation functions of general formal weighted double Hurwitz numbers coming from the Kadomtsev–Petviashvili tau functions of hypergeometric type (also known as Orlov–Scherbin partition functions). Notably, we use the change of variables suggested by the associated spectral curve, and our formula turns out to be a polynomial expression in a certain small set of formal functions defined on the spectral curve.
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Keywords: Hurwitz numbers, KP tau functions, Fock space
Mots-clés : Nombres de Hurwitz, tau fonction KP, espace de Fock
Boris Bychkov 1 ; Petr Dunin-Barkowski 2 ; Maxim Kazarian 3 ; Sergey Shadrin 4
CC-BY 4.0
@article{JEP_2022__9__1121_0,
author = {Boris Bychkov and Petr Dunin-Barkowski and Maxim Kazarian and Sergey Shadrin},
title = {Explicit closed algebraic formulas for {Orlov{\textendash}Scherbin} $n$-point functions},
journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques},
pages = {1121--1158},
publisher = {\'Ecole polytechnique},
volume = {9},
year = {2022},
doi = {10.5802/jep.202},
language = {en},
url = {https://jep.centre-mersenne.org/articles/10.5802/jep.202/}
}
TY - JOUR AU - Boris Bychkov AU - Petr Dunin-Barkowski AU - Maxim Kazarian AU - Sergey Shadrin TI - Explicit closed algebraic formulas for Orlov–Scherbin $n$-point functions JO - Journal de l’École polytechnique — Mathématiques PY - 2022 SP - 1121 EP - 1158 VL - 9 PB - École polytechnique UR - https://jep.centre-mersenne.org/articles/10.5802/jep.202/ DO - 10.5802/jep.202 LA - en ID - JEP_2022__9__1121_0 ER -
%0 Journal Article %A Boris Bychkov %A Petr Dunin-Barkowski %A Maxim Kazarian %A Sergey Shadrin %T Explicit closed algebraic formulas for Orlov–Scherbin $n$-point functions %J Journal de l’École polytechnique — Mathématiques %D 2022 %P 1121-1158 %V 9 %I École polytechnique %U https://jep.centre-mersenne.org/articles/10.5802/jep.202/ %R 10.5802/jep.202 %G en %F JEP_2022__9__1121_0
Boris Bychkov; Petr Dunin-Barkowski; Maxim Kazarian; Sergey Shadrin. Explicit closed algebraic formulas for Orlov–Scherbin $n$-point functions. Journal de l’École polytechnique — Mathématiques, Tome 9 (2022), pp. 1121-1158. doi : 10.5802/jep.202. https://jep.centre-mersenne.org/articles/10.5802/jep.202/
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