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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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2014 |
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| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2014
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| Online Zugang: | 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 |
| Zitieren: | 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| Zusammenfassung: | 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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| ISSN: | 1815-0659 |