Displaying similar documents to “Quantization and irreducible representations of infinite-dimensional transformation groups and Lie algebras.”

Explicit representations of classical Lie superalgebras in a Gelfand-Zetlin basis

N. I. Stoilova, J. Van der Jeugt (2011)

Banach Center Publications

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An explicit construction of all finite-dimensional irreducible representations of classical Lie algebras is a solved problem and a Gelfand-Zetlin type basis is known. However the latter lacks the orthogonality property or does not consist of weight vectors for 𝔰𝔬(n) and 𝔰𝔭(2n). In case of Lie superalgebras all finite-dimensional irreducible representations are constructed explicitly only for 𝔤𝔩(1|n), 𝔤𝔩(2|2), 𝔬𝔰𝔭(3|2) and for the so called essentially typical representations...

On the contraction of the discrete series of S U ( 1 , 1 )

C. Cishahayo, S. De Bièvre (1993)

Annales de l'institut Fourier

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It is shown, using techniques inspired by the method of orbits, that each non-zero mass, positive energy representation of the Poincaré group 𝒫 1 , 1 = S O ( 1 , 1 ) ⊗ s ℝ 2 can be obtained via contraction from the discrete series of representations of S U ( 1 , 1 ) .

Irreducible tensor representations of general linear Lie superalgebras

Tadeusz Józefiak (2009)

Colloquium Mathematicae

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We present a description of irreducible tensor representations of general linear Lie superalgebras in terms of generalized determinants in the symmetric and exterior superalgebras of a superspace over a field of characteristic zero.