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.


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