BGG diagrams for contact graded odd dimensional orthogonal geometries
Svatopluk Krýsl (2004)
Acta Universitatis Carolinae. Mathematica et Physica
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Svatopluk Krýsl (2004)
Acta Universitatis Carolinae. Mathematica et Physica
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Sagerschnig, Katja
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Summary: Let be a real semisimple -graded Lie algebra such that the Lie algebra cohomology group is contained in negative homogeneous degrees. We show that if we choose and denote by the parabolic subgroup determined by the grading, there is an equivalence between regular, normal parabolic geometries of type and filtrations of the tangent bundle, such that each symbol algebra is isomorphic to the graded Lie algebra . Examples of parabolic geometries determined by filtrations...
Somberg, Petr
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Lenka Zalabová, Vojtěch Žádník (2008)
Archivum Mathematicum
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The classical concept of affine locally symmetric spaces allows a generalization for various geometric structures on a smooth manifold. We remind the notion of symmetry for parabolic geometries and we summarize the known facts for -graded parabolic geometries and for almost Grassmannian structures, in particular. As an application of two general constructions with parabolic geometries, we present an example of non-flat Grassmannian symmetric space. Next we observe there is a distinguished...