Displaying similar documents to “Invariant nonassociative algebra structures on irreducible representations of simple Lie algebras.”

The Hurwitz determinants and the signatures of irreducible representations of simple real Lie algebras

Alexander Rudy (2005)

Open Mathematics

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The paper deals with the real classical Lie algebras and their finite dimensional irreducible representations. Signature formulae for Hermitian forms invariant relative to these representations are considered. It is possible to associate with the irreducible representation a Hurwitz matrix of special kind. So the calculation of the signatures is reduced to the calculation of Hurwitz determinants. Hence it is possible to use the Routh algorithm for the calculation.

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...