## The BGG diagram for contact orthogonal geometry of even dimension.(English)Zbl 1138.17310

Summary: BGG sequences are sequences of invariant differential operators acting on sections of vector bundles associated to a principal bundle locally modeled by $$G/P$$, where $$G$$ is a simple Lie group, $$P$$ its parabolic subgroup. They contain a large and important class of invariant differential operators in parabolic geometries. The BGG diagram contains the representation-theoretical information on the BGG sequence. We study its structure for $$G=\text{Spin}(2n,\mathbb C)$$ and its real forms, when $$P$$ is given by crossing the second root in the Dynkin or Satake diagram of $$G$$. We show that for certain real forms and certain representations the shape of the BGG diagram differs from the shape for the complex case.

### MSC:

 17B55 Homological methods in Lie (super)algebras 17B20 Simple, semisimple, reductive (super)algebras
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