A new set of on shell duality equations is proposed that leads to a map between strings moving on symmetric spaces with opposite curvatures. The transformation maps “waves” on a riemannian symmetric space M to “waves” on its dual riemannian symmetric space M̃ . This transformation preserves the energy momentum tensor though it is not a canonical transformation. The preservation of the energy mom...

We study the “Lie Algebra” of the group of Gauge Transformations of Space-time. We obtain topological invariants arising from this Lie Algebra. Our methods give us fresh mathematical points of view on Lorentz Transformations, orientation conventions, the Doppler shift, Pauli matrices, Electro-Magnetic Duality Rotation, Poynting vectors, and the Energy Momentum Tensor T .

When discussing spherically symmetric gravitational fields one usually assumes that the whole space-time is invariant under the 0 (3 ) group of transformations. In this paper, the Einstein field equations are investigated under the weaker assumption that only the 3-spaces t = const are 0 (3 ) symmetric. The following further assumptions are made: (1) The t lines are orthogonal to the spaces t =...

We consider the property of vanishing logarithmic term (VLT) for the fundamental solution of the shifted Laplace-d'Alembert operators + b (b a constant), on pseudo-Riemannian reductive symmetric spaces M. Our main result is that such an operator on the c-dual or Flensted-Jensen dual of M has the VLT property if and only if a corresponding operator on M does. For Lorentzian spaces, where the +b ...

The solvable Lie algebra parametrization of the symmetric spaces is discussed. Based on the solvable Lie algebra gauge two equivalent formulations of the symmetric space sigma model are studied. Their correspondence is established by inspecting the normalization conditions and deriving the field transformation laws.

We establish several conditions which are equivalent to |[Bx, x]| ≤ 〈Ax, x〉 , ∀x ∈ H , where A is a nonnegative operator and B is a complex symmetric operator on a separable complex Hilbert space H. Along the way, we also prove a new factorization theorem for complex symmetric operators. Mathematics Subject Classification (2000). 47B99.

= gp (v, v) , ∀v ∈ W, where Dp is Calabi’s diastasis function at p (the usual exponential expp obviously satisfied these equations when Dp is replaced by the square of the geodesics distance d2p from p). In this paper we prove that for every point p of an Hermitian symmetric space of noncompact type M there exists a globally defined diastatic exponential centered in p which is a diffeomorphism ...

The concept of range symmetric matrix is introduced in Minkowski space m. Equivalent conditions for a matrix to be range symmetric are determined. The existence of the Minkowski inverse of a range symmetric matrix in m is discussed.

In the context of the ring Q[x,y], of polynomials in 2n variables x = x1, . . . , xn and y = y1, . . . , yn, we introduce the notion of diagonally quasisymmetric polynomials. These, also called diagonal Temperley-Lieb invariants, make possible the further introduction of the space of diagonal Temperley-Lieb harmonics and diagonal Temperley-Lieb coinvariant space. We present new results and conj...