There is a ( ) 4' 4 UU × -bundle on four-dimensional square root Lorentz manifold. Then Pati-Salam model in curved space-time (Lagrangian) and gravity theory are constructed manifold based self-parallel transportation principle. An explicit formulation of Sheaf quantization this shown. superposition principle construct linear space space-time. The transition amplitude path integral given which ...

We prove that every surjective isometry from the unit sphere of a rank-2 Cartan factor C onto real Banach space Y, admits an extension to linear Y. The conclusion also covers case in which is spin factor. This result closes open problem and, combined with previous paper, allows us establish $$\hbox {JBW}^*$$ -triple M satisfies Mazur–Ulam property, is, its arbitrary Y

In this paper, we study the Cartan invariants for rank-one Cartan type Lie algebra W (1, n). This is done by reducing representations of generalized restricted Cartan type Lie algebra W (1, n) to representations of restricted Lie algebras W (1, 1) and of sl(2), and then extending Feldvoss-Nakano’s argument on W (1, 1) to the case W (1, n). Our discussion also shows some surprising difference be...

In this paper we consider some algebraic structures associated to a class of outer automorphisms of generalized Kac-Moody (GKM) algebras. These structures have recently been introduced in [2] for a smaller class of outer automorphisms in the case of ordinary Kac-Moody algebras with symmetrizable Cartan matrices. A GKM algebra G = G(A) is essentially described by its Cartan matrix, A = (aij)i,j∈...

We construct 16 reflection groups Γ acting on symmetric domains $\mathcal {D}$ of Cartan type IV, for which the graded algebras modular forms are freely generated by same weight, and in particular Satake-Baily-Borel compactification {D}/ {\Gamma }$ is isomorphic to a projective space. Four these previously known results Freitag-Salvati Manni, Matsumoto, Perna Runge. In addition we find several ...

We describe D = 4 twistorial membrane in terms of two twistorial three–dimensional world volume fields. We start with the D–dimensional p–brane generalizations of two phase space string formulations: due to Siegel, with two vectorial fourmomenta, and the formulation with tensorial momenta. Further we consider tensionful membrane case in D = 4. By using the membrane generalization of Cartan–Penr...

This is an outline of my lecture at the Hayama Symposium on several complex variables on December 21, 2002. The subject of the talk are new applications of the canonical Cartan connection for CR manifolds. Most of the results I will report on are based on joint research (partly in progress) with A.R. Gover and with J. Slovák and V. Souček. Partly, these results are specific for the class of CR ...