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  • 1
    Electronic Resource
    Electronic Resource
    Character formulas for irreducible modules of the Lie superalgebras sl(m/n) (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 2278-2304 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Kac distinguished between typical and atypical finite-dimensional irreducible representations of the Lie superalgebras sl(m/n) and provided an explicit character formula appropriate to all the typical representations. Here, the range of validity of some character formulas for atypical representations that have been proposed are discussed. Several of them are of the Kac–Weyl type, but then it is proved that all formulas of this type fail to correctly give the character of one particular atypical representation of sl(3/4). Having ruled out, therefore, all such formulas, a completely new extension of the Kac–Weyl character formula is proposed. The validity of this formula in the case of all covariant tensor irreducible representations is proved, and some evidence in support of the conjecture that it covers all irreducible representations of sl(m/n) is presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528637
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  • 2
    Electronic Resource
    Electronic Resource
    On the algebra of coupled SO(3) tensors (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 15-18 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The commutation relation for coupled SO(3) tensor operators is constructed. This gives rise to a Lie algebra for which 9j symbols appear in the structure constants. In an example it is shown how an exceptional Lie subalgebra can be realized. The closure requirement for the exceptional Lie algebra does not seem to be related to nontrivial 9j symbols but rather to vanishings of relations involving 6j symbols.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529993
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    New gradings of sl(3,C) representations (1989)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 30 (1989), S. 2763-2769 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Two new gradings of the Lie algebra sl(3,C) are the refined sl(2,C) and o(3) gradings. The grading in each case utilizes the sl(2,C), or o(3), weight together with a new additive modular label. A complete set of sl(3,C) representation basis states labeled by each to the two sets of additive quantum numbers is found. The newlabeling operator in both cases fails to commute with the cubic sl(3,C) Casimir operator, and hence mixes states of the contragredient representations (p,q) and (q,p)
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528510
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  • 4
    Electronic Resource
    Electronic Resource
    On the spectrum of a third-order SO(3) scalar in the enveloping algebra of SO(6) (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 802-805 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: With the aid of previously derived expressions for the SO(3) reduced matrix elements of the SO(6) generators, which were obtained by considering an intermediate SO(6)↓SU(2)⊗SU(2) reduction, a method is set up to evaluate analytic expressions for the eigenvalues of a third-order scalar operator belonging to the integrity basis of SO(3) scalar operators in the enveloping algebra of SO(6).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527973
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    Erratum: Regular subalgebras of Lie superalgebras and extended Dynkin diagrams [J. Math. Phys. 28, 292 (1987)] (1987)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 28 (1987), S. 2254-2254 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527409
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  • 6
    Electronic Resource
    Electronic Resource
    A pair of commuting scalars for G(2) &supuline; SU(2)×SU(2) (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 894-900 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: G(2) &supuline; SU(2)×SU(2) is a two-missing-labels problem, and therefore in order to give a complete and orthogonal specification of states of irreducible representations of G(2) in an SU(2)×SU(2) basis, one needs to find a pair of commuting Hermitian operators which are scalar with respect to the SU(2)×SU(2) subalgebra. A theorem due to Peccia and Sharp states that there are, apart from the Lie algebra invariants, twice as many functionally independent scalars as missing labels. Here two commuting SU(2)×SU(2) scalars are obtained, both of sixth order in the G(2) basis elements. They are in fact combinations of five scalars of different tensorial types, indicating that the functionally independent ones are in general insufficient to provide the lowest-order commuting scalars. An expression for the sixth-order invariant of G(2) is also obtained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.526545
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  • 7
    Electronic Resource
    Electronic Resource
    Irreducible representations of the exceptional Lie superalgebras D(2,1;α) (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 913-924 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The shift operator technique is used to give a complete analysis of all finite- and infinite-dimensional irreducible representations of the exceptional Lie superalgebras D(2,1;α). For all cases, the star or grade star conditions for the algebra are investigated. Among the finite-dimensional representations there are no star and only a few grade star representations, but an infinite class of infinite-dimensional star representations is found. Explicit expressions are given for the "doublet'' representation of D(2,1;α). The one missing label problem D(2,1;α)→su(2)+su(2)+su(2) is discussed in detail and solved explicitly.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.526547
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  • 8
    Electronic Resource
    Electronic Resource
    Group theoretical aspects of the extended interacting boson model (1987)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 28 (1987), S. 1644-1652 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Group theoretical aspects of the extended interacting boson model (gIBM) with s, d, and g bosons are discussed. The basis states and branching rules are given for the seven dynamical symmetries. Casimir operators and their eigenvalues are obtained and enable one to write down energy formulas.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527471
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  • 9
    Electronic Resource
    Electronic Resource
    Application of generating function techniques to Lie superalgebras (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 901-912 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The construction of generating functions for multiplicities of irreducible representations of Lie superalgebras from generating functions for characters is examined, and applied in order to obtain polynomial tensors and branching rules. Problems arising because of the existence of typical and atypical representations are discussed in detail. The techniques are applied to osp(1,2), spl(1,2), osp(3,2), and osp(4,2).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.526546
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    Paper (German National Licenses)
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  • 10
    Electronic Resource
    Electronic Resource
    A set of commuting missing label operators for SO(5)⊃SO(3) (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2124-2126 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The two-missing label problem for basis vectors of an SO(5) irreducible representation reduced according to the principal SO(3) subalgebra is considered. A pair of commuting Hermitian operators which are scalars with respect to the SO(3) subalgebra are explicitly constructed within the SO(5) enveloping algebra. One label generating operator is of fourth order and the other of sixth order in the SO(5) basis elements.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.526834
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