Classical Extended Conformal Algebras Associated with Constrained KP Hierarchy

Details Classical Extended Conformal Algebras Associated with Constrained KP Hierarchy Classical Extended Conformal Algebras Associated with Constrained KP Hierarchy

1994-10-21

arxiv.org/abs/hep-th/9410156v1

J.Math.Phys. 36 (1995) 2959-2971

Physics

High Energy Physics

High Energy Physics - Theory

NHCU-HEP-94-28, 19 pages (Plain TeX)

Scientific paper

10.1063/1.531004

We examine the conformal property of the second Hamiltonian structure of constrained KP hierarchy derived by Oevel and Strampp. We find that it naturallygives a family of nonlocal extended conformal algebras. We give two examples of such algebras and find that they are similar to Bilal's V algebra. By taking a gauge transformation one can map the constrained KP hierarchy to Kuperschmidt's nonstandard Lax hierarchy. We consider the second Hamiltonian structure in this representation. We show that after mapping the Lax operator to a pure differential operator the second structure becomes the sum of the second and the third Gelfand-Dickey brackets defined by this differential operator. We show that this Hamiltonian structure defines the W-U(1)-Kac-Moody algebra by working out its conformally covariant form.

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