Flag Manifolds
D. V. Alekseevsky (1997)
Zbornik Radova
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D. V. Alekseevsky (1997)
Zbornik Radova
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Šilhan, Josef
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From the text: The aim of this work is to advertise an algorithmic treatment of the computation of the cohomologies of semisimple Lie algebras. The base is Kostant’s result which describes the representation of the proper reductive subalgebra on the cohomologies space. We show how to (algorithmically) compute the highest weights of irreducible components of this representation using the Dynkin diagrams. The software package offers the data structures and corresponding procedures for...
Ivan Penkov, Vera Serganova (1989)
Annales de l'institut Fourier
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We compute the unique nonzero cohomology group of a generic - linearized locally free -module, where is the identity component of a complex classical Lie supergroup and is an arbitrary parabolic subsupergroup. In particular we prove that for this cohomology group is an irreducible -module. As an application we generalize the character formula of typical irreducible -modules to a natural class of atypical modules arising in this way.