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: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2014
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| 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862545756901081088 |
|---|---|
| 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. |
| collection | DSpace DC |
| 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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| first_indexed | 2025-11-25T07:13:19Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146849 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-25T07:13:19Z |
| publishDate | 2014 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| 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 |
| work_keys_str_mv | AT johanvandeleur then1reduceddkphierarchythestringequationandwconstraints AT johanvandeleur n1reduceddkphierarchythestringequationandwconstraints |