This paper treats a holomorphic self-mapping f : Ω → Ω of a bounded domain Ω in a separable Hilbert space H with a fixed point p. In case the domain is convex, we prove an infinitedimensional version of the Cartan-Carathéodory-Kaup-Wu Theorem. This is basically a rigidity result in the vein of the uniqueness part of the classical Schwarz lemma. The main technique, inspired by an old idea of H. ...

It is known that a family of transfer matrix functional equations, the T-system, can be compactly written in terms of the Cartan matrix of a simple Lie algebra. We formally replace this Cartan matrix of a simple Lie algebra with that of an affine Lie algebra, and then we obtain a system of functional equations different from the T-system. It may be viewed as an X (a) n type affine Toda field eq...

Definitions of non-relativistic conformal transformations are considered both in the Newton-Cartan and in the Kaluza-Klein-type Eisenhart/Bargmann geometrical frameworks. The symmetry groups that come into play are exemplified by the cosmological, and also the Newton-Hooke solutions of Newton’s gravitational field equations. It is shown, in particular, that the maximal symmetry group of the sta...

Gauge fields are described on an Riemann-Cartan space-time by means of tensorvalued differential forms and exterior calculus. It is shown that minimal coupling procedure leads to a gauge invariant theory where gauge fields interact with torsion, and that consistency conditions for the gauge fields impose restrictions in the nonRiemannian structure of space-time. The new results differ from the ...

In 1977, M. Matsumoto and R. Miron [9] constructed an orthonormal frame for an n-dimensional Finsler space, called ‘Miron frame’. The present authors [1, 2, 3, 10, 11] discussed four-dimensional Finsler spaces equipped with such frame. M. Matsumoto [7, 8] proved that in a three-dimensional Berwald space, all the main scalars are h-covariant constants and the h-connection vector vanishes. He als...

Let G be a semisimple noncompact Lie group with finite center and K a maximal compact subgroup ofG andX = G/K the corresponding Riemannian symmetric space of noncompact type. We have a Cartan decomposition g = k+ p and we choose a maximal abelian subalgebra a of p. In what follows, Σ corresponds to the root system of g and Σ+ to the positive roots. We have the root space decomposition g = g0 + ...

— Holonomic and semi-holonomic geometries modelled on a homogeneous space G/P are introduced as reductions of the holonomic or semi-holonomic frame bundles respectively satisfying a straightforward generalization of the partial differential equation characterizing torsion–free linear connections. Under a suitable regularity assumption on the model space G/P we establish an equivalence of catego...

In this paper, we perform a general reduction of an M2-brane on space–time that admits null Killing vector leading to fundamental string and D2-brane action in Newton–Cartan background.

In this work, we study direct limits of finite dimensional basic classical simple Lie superalgebras and obtain the conjugacy classes of Cartan subalgebras under the group of automorphisms.