ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
The algebra Xi of nonlinear (local and nonlocal) differential operators, acting on the ring of analytic functions, is studied. It is shown in particular that this space splits into 3×2 special subalgebras ∑jr, j=0,±1, r=±1. Each subalgebra is completely specified by quantum numbers s and (p,q) describing the conformal spin, and the lowest and the highest degrees, respectively. The algebra ∑++ (and its dual ∑−−) of local (pure nonlocal) differential operators is used to calculate the general expression of the Gelfand–Dickey bracket and the Wn-symmetry Poisson, one in terms of a set of spin j canonical fields uj, 2≤j≤n and a nonlinear u-cubic dependent differential operator D(n,i,j;z,u). The explicit form of this operator is worked out. Other remarkable features are also discussed.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.530461
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