Quantum KdV hierarchy and quasimodular forms

IF 16.4 1区 化学 Q1 CHEMISTRY, MULTIDISCIPLINARY
Jan-Willem M. van Ittersum, Giulio Ruzza
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引用次数: 0

Abstract

Dubrovin $\href{https://doi.org/10.1007/s00023-015-0449-2}{[10]}$ has shown that the spectrum of the quantization (with respect to the first Poisson structure) of the dispersionless Korteweg–de Vries (KdV) hierarchy is given by shifted symmetric functions; the latter are related by the Bloch–Okounkov Theorem $\href{https://doi.org/10.1007/JHEP07(2014)141}{[1]}$ to quasimodular forms on the full modular group. We extend the relation to quasimodular forms to the full quantum KdV hierarchy (and to the more general quantum Intermediate Long Wave hierarchy). These quantum integrable hierarchies have been defined by Buryak and Rossi $\href{https://doi.org/10.1007/s11005-015-0814-6}{[6]}$ in terms of the double ramification cycle in the moduli space of curves. The main tool and conceptual contribution of the paper is a general effective criterion for quasimodularity.
量子 KdV 层次和准模态
Dubrovin $\href{https://doi.org/10.1007/s00023-015-0449-2}{[10]}$ 证明了无色散 Korteweg-de Vries(KdV)层次结构的量子化频谱(关于第一泊松结构)是由移位对称函数给出的;后者通过布洛赫-奥孔科夫定理 $\href{https://doi.org/10.1007/JHEP07(2014)141}{[1]}$ 与全模组上的准模态相关。我们把准模形式的关系扩展到完整的量子 KdV 层次(以及更一般的量子中间长波层次)。布里亚克和罗西 $\href{https://doi.org/10.1007/s11005-015-0814-6}{[6]}$ 用曲线模空间的双斜面循环定义了这些量子可积分层次。本文的主要工具和概念贡献是准模性的一般有效准则。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Accounts of Chemical Research
Accounts of Chemical Research 化学-化学综合
CiteScore
31.40
自引率
1.10%
发文量
312
审稿时长
2 months
期刊介绍: Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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