On tau-functions for the KdV hierarchy

被引：0
作者：
Boris Dubrovin
Di Yang
Don Zagier
机构：
[1] SISSA,School of Mathematical Sciences
[2] University of Science and Technology of China,undefined
[3] Max-Planck-Institut für Mathematik,undefined
[4] International Centre for Theoretical Physics,undefined
来源：
Selecta Mathematica | 2021年 / 27卷
关键词：
KdV hierarchy; Tau-function; Pair of wave functions; Matrix resolvent; Generating series; 37K10; 53D45; 14N35; 05A15; 33E15;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
For an arbitrary solution to the KdV hierarchy, the generating series of logarithmic derivatives of the tau-function of the solution can be expressed by the basic matrix resolvent via algebraic manipulations. Based on this we develop in this paper two new formulae for the generating series by introducing a pair of wave functions of the solution. Applications to the Witten–Kontsevich tau-function, to the generalized Brézin–Gross–Witten (BGW) tau-function, as well as to a modular deformation of the generalized BGW tau-function which we call the Lamé tau-function are also given.
引用
收藏
相关论文
共 105 条
[1]  
Adler M(1992)A matrix integral solution to two-dimensional Commun. Math. Phys. 147 25-56
[2]  
van Moerbeke P(2018)-gravity Adv. Theor. Math. Phys. 22 1347-1399
[3]  
Alexandrov A(2017)Cut-and-join description of generalized Brezin-Gross-Witten model Lett. Math. Phys. 107 1837-1857
[4]  
Balogh F(1993)Geometric interpretation of Zhou’s explicit formula for the Witten–Kontsevich tau function J. Stat. Phys. 73 415-421
[5]  
Yang D(2017)Variance calculations and the Bessel kernel Ann. Henri Poincaré 18 3193-3248
[6]  
Basor EL(2018)Integrable differential systems of topological type and reconstruction by the topological recursion Ann. Henri Poincaré 19 141-161
[7]  
Tracy CA(2015)Loop equations from differential systems on curves Ann. Henri Poincaré 16 2713-2782
[8]  
Belliard R(2017)Rational differential systems, loop equations, and application to the qth reductions of KP Commun. Math. Phys. 352 585-619
[9]  
Eynard B(2016)The Kontsevich matrix integral: Convergence to the Painlevé hierarchy and Stokes’ phenomenon Phys. D Nonlinear Phenomena 327 30-57
[10]  
Marchal O(2018)Correlation functions of the KdV hierarchy and applications to intersection numbers over IMRN 2018 1368-1410
12345678910