) 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
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.
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...
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...
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...
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...
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...