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On the Cartan-Norden theorem for affine Kähler immersions

Maria Robaszewska (2000)

Annales Polonici Mathematici

In [O2] the Cartan-Norden theorem for real affine immersions was proved without the non-degeneracy assumption. A similar reasoning applies to the case of affine Kähler immersions with an anti-complex shape operator, which allows us to weaken the assumptions of the theorem given in [NP]. We need only require the immersion to have a non-vanishing type number everywhere on M.

On the composition structure of the twisted Verma modules for 𝔰𝔩 ( 3 , )

Libor Křižka, Petr Somberg (2015)

Archivum Mathematicum

We discuss some aspects of the composition structure of twisted Verma modules for the Lie algebra 𝔰𝔩 ( 3 , ) , including the explicit structure of singular vectors for both 𝔰𝔩 ( 3 , ) and one of its Lie subalgebras 𝔰𝔩 ( 2 , ) , and also of their generators. Our analysis is based on the use of partial Fourier tranform applied to the realization of twisted Verma modules as D -modules on the Schubert cells in the full flag manifold for SL ( 3 , ) .

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