Decomposing oscillator representations of by a super dual pair
Kyo Nishiyama (1991)
Compositio Mathematica
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Displaying similar documents to “Invariant nonassociative algebra structures on irreducible representations of simple Lie algebras.”
Decomposing oscillator representations of by a super dual pair
Matrix elements and highest weight Wigner coefficients of
W. H. Klink, T. Ton-That (1982)
Annales de l'I.H.P. Physique théorique
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Orthogonal polynomial bases for holomorphically induced representations of the general linear groups
W. H. Klink, T. Ton-That (1979)
Annales de l'I.H.P. Physique théorique
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Infinite dimensional Lie algebras: representations and applications
Goddard, P.
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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...
Irreducible identities of -algebras.
Rotkiewicz, M. (2003)
Acta Mathematica Universitatis Comenianae. New Series
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Super boson-fermion correspondence
Victor G. Kac, J. W. Van de Leur (1987)
Annales de l'institut Fourier
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We establish a super boson-fermion correspondence, generalizing the classical boson-fermion correspondence in 2-dimensional quantum field theory. A new feature of the theory is the essential non-commutativity of bosonic fields. The superbosonic fields obtained by the super bosonization procedure from super fermionic fields form the affine superalgebra . The converse, super fermionization procedure, requires introduction of the super vertex operators. As applications, we give vertex...