The space of the global sections chiral de Rham complex on a compact Ricci-flat Kähler manifold is calculated and it expressed as subspace invariant elements in $$\beta \gamma -bc$$ system under action certain Lie algebra Cartan type.

We suggest to use " minimal " choice of quantum gravity theory, that is the quantum field theory, in which space-time is seen as Rie-mannian space and metrics (or vierbein field) is the dynamical variable. We then suggest to use the simplest acceptable action, that is the squared curvature action. The correspondent model is renor-malizable, has the correct classical limit and can be explored us...

Külshammer, Olsson and Robinson conjectured that a certain set of numbers determined the invariant factors of the `-Cartan matrix for Sn (equivalently, the invariant factors of the Cartan matrix for the Iwahori-Hecke algebra Hn(q), where q is a primitive `th root of unity). We call these invariant factors Cartan invariants. In a previous paper, the second author calculated these Cartan invarian...

An explicit, geometric description of the first-class constraints and their Poisson brackets for gravity in Palatini-Cartan formalism (in space-time dimension greater than three) is given. The corresponding Batalin- Fradkin-Vilkovisky (BFV) formulation also developed.

Abstract In this continuation of [4], we investigate the deformations holomorphic Cartan geometries where underlying complex manifold is allowed to move. The space infinitesimal a flat geometry computed. We show that natural forgetful map, from principal bundle on topological manifold, an isomorphism.