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  • 1
    Electronic Resource
    Electronic Resource
    Finite-dimensional irreducible representations of reflection algebra for su(1,1)q vertex model: Classification, boson–fermion realizations, and Yang–Baxterization (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 6150-6157 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Finite-dimensional irreducible representations of a reflection algebra related to the reflection equation for the su(1,1)q model are classified. It is proven that this algebra has two inequivalent one-dimensional and one two-dimensional irreducible representations. Some indecomposable representations are also constructed and the (q-boson–)fermion realizations are explicitly presented. Finally, the Yang–Baxterization of this algebra and its constant solutions (the one-dimensional representations) is investigated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530734
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  • 2
    Electronic Resource
    Electronic Resource
    The q-boson realization of parametrized cyclic representations of quantum algebras at qp = 1 (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 427-435 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A parametrized cyclic representation of the q-deformed Heisenberg–Weyl algebras is constructed. The cyclic representations of any quantum algebras are studied in terms of their q-boson realizations. A general method to construct the q-boson realizations of quantum algebras from their Verma representations is proposed. Two explicit examples sl(2)q and sl(3)q are studied in detail. Some cyclic representations of quantum algebras sl(n)q and UqCn are presented by using their q-boson realizations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529832
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  • 3
    Electronic Resource
    Electronic Resource
    New inhomogeneous boson realizations and inhomogeneous differential realizations of Lie algebras (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 2797-2802 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The inhomogeneous boson realizations (IHBR) and the corresponding inhomogeneous differential realizations (IHDR) of Lie algebras, which play an important role in the search of quasi-exactly solvable problems (QESP) of quantum mechanics, are studied. All possible IHDR of semisimple Lie algebras can be obtained in this way. As examples, the IHBR and the corresponding IHDR of Lie algebras SU(2) and SU(3) are studied in detail.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528982
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  • 4
    Electronic Resource
    Electronic Resource
    Negative binomial and multinomial states: Probability distributions and coherent states (1997)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 3968-3987 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Following the relationship between probability distribution and coherent states, for example the well known Poisson distribution and the ordinary coherent states and relatively less known one of the binomial distribution and the su(2) coherent states, we propose interpretation of su(1,1) and su(r,1) coherent states in terms of probability theory. They will be called the negative binomial (multinomial) states which correspond to the negative binomial (multinomial) distribution, the non-compact counterpart of the well known binomial (multinomial) distribution. Explicit forms of the negative binomial (multinomial) states are given in terms of various boson representations which are naturally related to the probability theory interpretation. Here, we show fruitful interplay of probability theory, group theory, and quantum theory. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532102
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  • 5
    Electronic Resource
    Electronic Resource
    Hypergeometric states and their nonclassical properties (1997)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 2154-2166 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: "Hypergeometric states," which are a one-parameter generalization of binomial states of the single-mode quantized radiation field, are introduced and their nonclassical properties are investigated. Their limits to the binomial states and to the coherent and number states are studied. The ladder operator formulation of the hypergeometric states is found and the algebra involved turns out to be a one-parameter deformation of su(2) algebra. These states exhibit highly nonclassical properties, like sub-Poissonian character, antibunching, and squeezing effects. The quasiprobability distributions in phase space, namely the Q and the Wigner functions are studied in detail. These remarkable properties seem to suggest that the hypergeometric states deserve further attention from theoretical and applicational sides of quantum optics.© 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.531965
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  • 6
    Electronic Resource
    Electronic Resource
    Inhomogeneous boson realization of indecomposable representations of Lie algebras (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 287-293 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: By making use of the differential realization of Lie algebras in the space of inhomogeneous polynomials of a certain number of variables, the corresponding inhomogeneous boson realization of Lie algebras is given. A new kind of indecomposable representations of Lie algebras are studied on the universal enveloping algebra of Heisenberg–Weyl algebra, its subspaces and its quotient spaces. The finite-dimensional representations are naturally obtained on the subspaces of Fock space. As an example, the indecomposable and irreducible representations of the Lie algebra su(2) are discussed in detail.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528912
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  • 7
    Electronic Resource
    Electronic Resource
    Inhomogeneous differential realization, boson–fermion realization of Lie superalgebras and their indecomposable representations (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 767-775 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: An inhomogeneous differential realization (IHDR) of Lie superalgebras, which plays an important role in the search for quasi-exactly solvable problems (QESP) of quantum mechanics, is studied. The corresponding inhomogeneous boson–fermion realization (IHBFR) of Lie superalgebras is obtained. By making use of the IHBFR, a new kind of indecomposable and irreducible representations of Lie superalgebras is studied on the universal enveloping algebra of Heisenberg–Weyl superalgebra, and on its subspaces and quotient spaces. The finite dimensional representations of Lie superalgebras are naturally obtained on the subspaces of Fock space. As examples, the IHDR of Lie superalgebra spl(m,1) is given, and the indecomposable and irreducible representations of Lie superalgebra su(2,1) are studied in detail.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529369
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  • 8
    Electronic Resource
    Electronic Resource
    Excited Binomial States and Excited Negative Binomial States of the Radiation Field and Some of Their Statistical Properties (2000)
    Springer
    International journal of theoretical physics 39 (2000), S. 1437-1444 
    Details
    ISSN: 1572-9575
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We introduce excited binomial states and excited negative binomial states of theradiation field by repeated application of the photon creation operator on binomialstates and negative binomial states. They reduce to Fock states and excitedcoherent states in certain limits and can be viewed as intermediate states betweenFock states and coherent states. We find that both the excited binomial statesand excited negative binomial states can be exactly normalized in terms ofhypergeometric functions. Base on this interesting characteristic, some of thestatistical properties are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1003619724681
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  • 9
    Electronic Resource
    Electronic Resource
    Construction of cyclic representations of quantum algebras at q p =1 from their regular representations (1992)
    Springer
    Letters in mathematical physics 25 (1992), S. 277-286 
    Details
    ISSN: 1573-0530
    Keywords: 17B10 ; 17B37
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Cyclic representations of maximal dimension of the quantum algebra U q L associated with any finite-dimensional simple Lie algebra L are studied from its regular representation at q p =1, which is proved to be a quotient module of itself as a left module with respect to some submodules. The general theory is given after an instructive example U q sl(2) is studied. Another explicit example U q sl(3) is also presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00398400
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  • 10
    Electronic Resource
    Electronic Resource
    The cyclic representations of the quantum superalgebra U q osp(2, 1) withq a root of unity (1991)
    Springer
    Letters in mathematical physics 23 (1991), S. 19-27 
    Details
    ISSN: 1573-0530
    Keywords: 22E99 ; 81Q99
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract By generalizing De Concini and Kac's cyclic representation theory of quantum groups at roots of unity, the cyclic representations of the quantum superalgebra U q osp(2, 1) are constructed in three classes: irreducible representations with single multiplicities, irreducible representations with the multiplicities larger than one, and indecomposable representations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01811290
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