Journal of Nonlinear Mathematical Physics

Volume 10, Issue 2, May 2003

1. Representations of the Conformal Lie Algebra in the Space of Tensor Densities on the Sphere

Pascal REDOU
Pages: 136 - 140
Let F(Sn ) be the space of tensor densities on Sn of degree . We consider this space as an induced module of the nonunitary spherical series of the group SO0(n+1, 1) and classify (so(n+1, 1), SO(n+1))-simple and unitary submodules of F(Sn ) as a function of .

2. Superconformal Algebras and Lie Superalgebras of the Hodge Theory

E POLETAEVA
Pages: 141 - 147
We observe a correspondence between the zero modes of superconformal algebras S (2, 1) and W(4) ([8]) and the Lie superalgebras formed by classical operators apearing in the Kähler and hyper-Kähler geometry.

3. Deformations of Modules of Differential Forms

B AGREBAOUI, M BEN AMMAR, N BEN FRAJ, V OVSIENKO
Pages: 148 - 156
We study non-trivial deformations of the natural action of the Lie algebra Vect(Rn ) on the space of differential forms on Rn . We calculate abstractions for integrability of ifinitesimal multi-parameter deformations and determine the commutative associative algebra corresponding to the miniversal deformation...

4. Periodic Solutions of a Many-Rotator Problem in the Plane. II. Analysis of Various Motions

F CALOGERO, J-P FRANC¸OISE, M SOMMACAL
Pages: 157 - 214
Various solutions are displayed and analyzed (both analytically and numerically) of a recently-introduced many-body problem in the plane which includes both integrable and nonintegrable cases (depending on the values of the coupling constants); in paticular the origin of certain periodic behaviors is...

5. A Unified Description of the Asymmetric q-PV and d-PIV Equations and their Schlesinger Transformations

B GRAMMATICOS, A RAMANI, Y OHTA
Pages: 215 - 228
We present a geometric description, based on the affine Weyl group E (1) 6 , of two discrete analogues of the Painlevé VI equation, known as the asymmetric q-PV and asymmetric d-PIV. This approach allows us to describe in a unified way the evolution of the mapping along the independent variable and along...

6. Towards a Theory of Differential Constraints of a Hydrodynamic Hierarchy

L. Martinez-Alonso, A B SHABAT
Pages: 229 - 242
We present a theory of compatible differential constraints of a hydrodynamic hierarchy of infinite-dimensional systems. It provides a convenient point of view for studying and formulating integrability properties and it reveals some hidden structures of the theory of integrable systems. Illustrative...

7. Fine Structure of the Discrete Transformation for Multicomponent Integrable Systems

A N LEZNOV, J ESCOBEDO-ALATORRE, R TORRES-CORDOBA
Pages: 243 - 251
It is shown that in the case of multicomponent integrable systems connected with algebras An, the discrete transformation T possesses the fine structure and can be represented in the form T = Tli i , where Ti are n commuting basis discrete transfomations and li are arbitrary natural numbers. All the...