Kac-Schwarz operators of type B, quantum spectral curves, and spin Hurwitz numbers

被引：2

作者：

Ji, Ce ^{[1
]}

Wang, Zhiyuan ^{[1
]}

Yang, Chenglang ^{[1
,2
]}

机构：

[1] Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China

[2] Peking Univ, Beijing Int Ctr Math Res, Beijing 100871, Peoples R China

来源：

JOURNAL OF GEOMETRY AND PHYSICS | 2023年 / 189卷

关键词：

BKP hierarchy; Affine coordinates; Kac-Schwarz operators; Quantum spectral curve; Spin Hurwitz numbers; GEOMETRIC INTERPRETATION; TOPOLOGICAL RECURSION; TODA EQUATIONS; FORMULA;

D O I：

10.1016/j.geomphys.2023.104831

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Given a tau-function tau(t) of the BKP hierarchy satisfying tau(0) = 1, we discuss the relation between its BKP-affine coordinates on the isotropic Sato Grassmannian and its BKP-wave function. Using this result, we formulate a type of Kac-Schwarz operators for tau (t) in terms of BKP-affine coordinates. As an example, we compute the affine coordinates of the BKP tau-function for spin single Hurwitz numbers with completed cycles, and find a pair of Kac-Schwarz operators (P, Q ) satisfying [P, Q ] = 1. By doing this, we obtain the quantum spectral curve for spin single Hurwitz numbers.(c) 2023 Elsevier B.V. All rights reserved.

引用

页数：20

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