And algebras, and Ward identities
Elsevier, 2023
Online
academicJournal
Zugriff:
It was demonstrated recently that the W1+∞ algebra contains commutative subalgebras associated with all integer slope rays (including the vertical one). In this paper, we realize that every element of such a ray is associated with a generalized W˜ algebra. In particular, the simplest commutative subalgebra associated with the rational Calogero Hamiltonians is associated with the W˜ algebras studied earlier. We suggest a definition of the generalized W˜ algebra as differential operators in variables pk basing on the matrix realization of the W1+∞ algebra, and also suggest an unambiguous recursive definition, which, however, involves more elements of the W1+∞ algebra than is contained in its commutative subalgebras. The positive integer rays are associated with W˜ algebras that form sets of Ward identities for the WLZZ matrix models, while the vertical ray associated with the trigonometric Calogero-Sutherland model describes the hypergeometric τ-functions corresponding to the completed cycles.
Titel: |
And algebras, and Ward identities
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Autor/in / Beteiligte Person: | Drachov, Ya. ; Mironov, A. ; Popolitov, A. |
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Veröffentlichung: | Elsevier, 2023 |
Medientyp: | academicJournal |
DOI: | 10.1016/j.physletb.2023.138426 |
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