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Maslov indices on the metaplectic group M p ( n )

Maurice De Gosson (1990)

Annales de l'institut Fourier

We use the properties of M p ( n ) to construct functions μ : M p ( n ) Z 8 associated with the elements of the lagrangian grassmannian Λ (n) which generalize the Maslov index on Mp(n) defined by J. Leray in his “Lagrangian Analysis”. We deduce from these constructions the identity between M p ( n ) and a subset of S p ( n ) × Z 8 , equipped with appropriate algebraic and topological structures.

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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