Volume 10, Issue 2, May 2003
Pages: 136 - 140
) 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
Pages: 141 - 147
We observe a correspondence between the zero modes of superconformal algebras
S (2, 1) and W(4) () and the Lie superalgebras formed by classical operators apearing in the Kähler and hyper-Kähler geometry.
Pages: 148 - 156
We study non-trivial deformations of the natural action of the Lie algebra Vect(Rn
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...
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...
Pages: 215 - 228
We present a geometric description, based on the affine Weyl group E
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...
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...
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...