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Singular BGG sequences for the even orthogonal case

Lukáš KrumpVladimír Souček — 2006

Archivum Mathematicum

Locally exact complexes of invariant differential operators are constructed on the homogeneous model for a parabolic geometry for the even orthogonal group. The tool used for the construction is the Penrose transform developed by R. Baston and M. Eastwood. Complexes constructed here belong to the singular infinitesimal character.

On a new normalization for tractor covariant derivatives

Matthias HammerlPetr SombergVladimír SoučekJosef Šilhan — 2012

Journal of the European Mathematical Society

A regular normal parabolic geometry of type G / P on a manifold M gives rise to sequences D i of invariant differential operators, known as the curved version of the BGG resolution. These sequences are constructed from the normal covariant derivative ω on the corresponding tractor bundle V , where ω is the normal Cartan connection. The first operator D 0 in the sequence is overdetermined and it is well known that ω yields the prolongation of this operator in the homogeneous case M = G / P . Our first main result...

Fischer decompositions in Euclidean and Hermitean Clifford analysis

Freddy BrackxHennie de SchepperVladimír Souček — 2010

Archivum Mathematicum

Euclidean Clifford analysis is a higher dimensional function theory studying so–called monogenic functions, i.e. null solutions of the rotation invariant, vector valued, first order Dirac operator ̲ . In the more recent branch Hermitean Clifford analysis, this rotational invariance has been broken by introducing a complex structure J on Euclidean space and a corresponding second Dirac operator ̲ J , leading to the system of equations ̲ f = 0 = ̲ J f expressing so-called Hermitean monogenicity. The invariance of this...

Hasse diagrams for parabolic geometries

Krump, LukášSouček, Vladimír — 2003

Proceedings of the 22nd Winter School "Geometry and Physics"

The invariant differential operators on a manifold with a given parabolic structure come in two classes, standard and non-standard, and can be further subdivided into regular and singular ones. The standard regular operators come in repeated patterns, the Bernstein-Gelfand-Gelfand sequences, described by Hasse diagrams. In this paper, the authors present an alternative characterization of Hasse diagrams, which is quite efficient in the case of low gradings. Several examples are given.

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