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Displaying similar documents to “Induced modules for affine Lie algebras.”

The F-method and a branching problem for generalized Verma modules associated to ( Lie G 2 , so ( 7 ) )

Todor Milev, Petr Somberg (2013)

Archivum Mathematicum

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The branching problem for a couple of non-compatible Lie algebras and their parabolic subalgebras applied to generalized Verma modules was recently discussed in [15]. In the present article, we employ the recently developed F-method, [10], [11] to the couple of non-compatible Lie algebras Lie G 2 ↪ i so ( 7 ) , and generalized conformal so ( 7 ) -Verma modules of scalar type. As a result, we classify the i ( Lie G 2 ) ∩ 𝔭 -singular vectors for this class of so ( 7 ) -modules.

On bounded generalized Harish-Chandra modules

Ivan Penkov, Vera Serganova (2012)

Annales de l’institut Fourier

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Let 𝔤 be a complex reductive Lie algebra and 𝔨 ⊂ 𝔤 be any reductive in 𝔤 subalgebra. We call a ( 𝔤 , 𝔨 ) -module M bounded if the 𝔨 -multiplicities of M are uniformly bounded. In this paper we initiate a general study of simple bounded ( 𝔤 , 𝔨 ) -modules. We prove a strong necessary condition for a subalgebra 𝔨 to be bounded (Corollary 4.6), to admit an infinite-dimensional simple bounded ( 𝔤 , 𝔨 ) -module, and then establish a sufficient condition for a subalgebra 𝔨 to be bounded (Theorem 5.1). As a result we are...