The Hodge-FVH correspondence-Reference-Cited by-同舟云学术

The Hodge-FVH correspondence

Published:2021-02-23 Issue:0 Volume:0 Page:
ISSN:1435-5345
Container-title:Journal für die reine und angewandte Mathematik
language:en
Short-container-title:

Author:

Liu Si-Qi¹,Yang Di²,Zhang Youjin¹,Zhou Chunhui²

Affiliation:

1. Department of Mathematical Sciences , Tsinghua University , Beijing 100084 , P. R. China

2. School of Mathematical Sciences , University of Science and Technology of China , Hefei 230026 , P. R. China

Abstract

Abstract The Hodge-FVH correspondence establishes a relationship between the special cubic Hodge integrals and an integrable hierarchy, which is called the fractional Volterra hierarchy. In this paper we prove this correspondence. As an application of this result, we prove a gap condition for certain special cubic Hodge integrals and give an algorithm for computing the coefficients that appear in the gap condition.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Mathematics

Reference36 articles.

1. M. Adler, T. Shiota and P. van Moerbeke, A Lax representation for the vertex operator and the central extension, Comm. Math. Phys. 171 (1995), no. 3, 547–588.

2. B. Bakalov and W. Wheeless, Additional symmetries of the extended bigraded Toda hierarchy, J. Phys. A 49 (2016), no. 5, Article ID 055201.

3. A. Brini, Open topological strings and integrable hierarchies: Remodeling the A-model, Comm. Math. Phys. 312 (2012), no. 3, 735–780.

4. A. Buryak, Dubrovin–Zhang hierarchy for the Hodge integrals, Commun. Number Theory Phys. 9 (2015), no. 2, 239–272.

5. E. Date, M. Kashiwara, M. Jimbo and T. Miwa, Transformation groups for soliton equations, Nonlinear integrable systems—classical theory and quantum theory (Kyoto 1981), World Science, Singapore (1983), 39–119.

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