Displaying similar documents to “On certain class of unitarizable representations of the Lie algebra u ( p , q ) ”

Classification of irreducible weight modules

Olivier Mathieu (2000)

Annales de l'institut Fourier

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Let 𝔤 be a reductive Lie algebra and let 𝔥 be a Cartan subalgebra. A 𝔤 -module M is called a if and only if M = ⊕ λ M λ , where each weight space M λ is finite dimensional. The main result of the paper is the classification of all simple weight 𝔤 -modules. Further, we show that their characters can be deduced from characters of simple modules in category 𝒪 .

Norm estimates for unitarizable highest weight modules

Bernhard Krötz (1999)

Annales de l'institut Fourier

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We consider families of unitarizable highest weight modules ( ℋ λ ) λ ∈ L on a halfline L . All these modules can be realized as vector valued holomorphic functions on a bounded symmetric domain 𝒟 , and the polynomial functions form a dense subset of each module ℋ λ , λ ∈ L . In this paper we compare the norm of a fixed polynomial in two Hilbert spaces corresponding to two different parameters. As an application we obtain that for all λ ∈ L the module of hyperfunction vectors ℋ λ - ∞ can be realized as the space of...

On representations of restricted Lie superalgebras

Yu-Feng Yao (2014)

Czechoslovak Mathematical Journal

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Simple modules for restricted Lie superalgebras are studied. The indecomposability of baby Kac modules and baby Verma modules is proved in some situation. In particular, for the classical Lie superalgebra of type A ( n | 0 ) , the baby Verma modules Z χ ( λ ) are proved to be simple for any regular nilpotent p -character χ and typical weight λ . Moreover, we obtain the dimension formulas for projective covers of simple modules with p -characters of standard Levi form.