The (n,1)-Reduced DKP Hierarchy, the String Equation and W Constraints

The total descendent potential of a simple singularity satisfies the Kac-Wakimoto principal hierarchy. Bakalov and Milanov showed recently that it is also a highest weight vector for the corresponding W-algebra. This was used by Liu, Yang and Zhang to prove its uniqueness. We construct this principa...

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Опубліковано в: :Symmetry, Integrability and Geometry: Methods and Applications
Дата:2014
Автор: Johan van de Leur
Формат: Стаття
Мова:Англійська
Опубліковано: Інститут математики НАН України 2014
Онлайн доступ:https://nasplib.isofts.kiev.ua/handle/123456789/146849
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:The (n,1)-Reduced DKP Hierarchy, the String Equation and W Constraints / Johan van de Leur // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 26 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Johan van de Leur
author_facet Johan van de Leur
citation_txt The (n,1)-Reduced DKP Hierarchy, the String Equation and W Constraints / Johan van de Leur // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 26 назв. — англ.
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container_title Symmetry, Integrability and Geometry: Methods and Applications
description The total descendent potential of a simple singularity satisfies the Kac-Wakimoto principal hierarchy. Bakalov and Milanov showed recently that it is also a highest weight vector for the corresponding W-algebra. This was used by Liu, Yang and Zhang to prove its uniqueness. We construct this principal hierarchy of type D in a different way, viz. as a reduction of some DKP hierarchy. This gives a Lax type and a Grassmannian formulation of this hierarchy. We show in particular that the string equation induces a large part of the W constraints of Bakalov and Milanov. These constraints are not only given on the tau function, but also in terms of the Lax and Orlov-Schulman operators.
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institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
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language English
last_indexed 2025-11-25T07:13:19Z
publishDate 2014
publisher Інститут математики НАН України
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spelling Johan van de Leur
2019-02-11T17:10:32Z
2019-02-11T17:10:32Z
2014
The (n,1)-Reduced DKP Hierarchy, the String Equation and W Constraints / Johan van de Leur // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 26 назв. — англ.
1815-0659
2010 Mathematics Subject Classification: 17B69; 17B80; 53D45; 81R10
DOI:10.3842/SIGMA.2014.007
https://nasplib.isofts.kiev.ua/handle/123456789/146849
The total descendent potential of a simple singularity satisfies the Kac-Wakimoto principal hierarchy. Bakalov and Milanov showed recently that it is also a highest weight vector for the corresponding W-algebra. This was used by Liu, Yang and Zhang to prove its uniqueness. We construct this principal hierarchy of type D in a different way, viz. as a reduction of some DKP hierarchy. This gives a Lax type and a Grassmannian formulation of this hierarchy. We show in particular that the string equation induces a large part of the W constraints of Bakalov and Milanov. These constraints are not only given on the tau function, but also in terms of the Lax and Orlov-Schulman operators.
This paper is a contribution to the Special Issue in honor of Anatol Kirillov and Tetsuji Miwa. The full
 collection is available at http://www.emis.de/journals/SIGMA/InfiniteAnalysis2013.html.
 
 I would like to thank Bojko Bakalov for useful discussions and the three referees for valuable
 suggestions, which improved the paper.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
The (n,1)-Reduced DKP Hierarchy, the String Equation and W Constraints
Article
published earlier
spellingShingle The (n,1)-Reduced DKP Hierarchy, the String Equation and W Constraints
Johan van de Leur
title The (n,1)-Reduced DKP Hierarchy, the String Equation and W Constraints
title_full The (n,1)-Reduced DKP Hierarchy, the String Equation and W Constraints
title_fullStr The (n,1)-Reduced DKP Hierarchy, the String Equation and W Constraints
title_full_unstemmed The (n,1)-Reduced DKP Hierarchy, the String Equation and W Constraints
title_short The (n,1)-Reduced DKP Hierarchy, the String Equation and W Constraints
title_sort (n,1)-reduced dkp hierarchy, the string equation and w constraints
url https://nasplib.isofts.kiev.ua/handle/123456789/146849
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