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  • 1
    Electronic Resource
    Electronic Resource
    Orbit–orbit branching rules between classical simple Lie algebras and maximal reductive subalgebras (1996)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 37 (1996), S. 6570-6581 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Complete orbit–orbit branching rules are found for the classical algebra–maximal reductive subalgebra pairs Am+n+1⊃Am⊕An⊕u(1), Bm+1⊃Bm⊕u(1), Cm+1⊃Am⊕u(1), Dm+1⊃Dm⊕u(1), and Dm+1⊃Am⊕u(1). © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.531746
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  • 2
    Electronic Resource
    Electronic Resource
    Weyl orbits and their expansions in irreducible representations for affine Kac–Moody algebras (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 2343-2356 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Weyl orbits of affine rank 2 and 3 algebras are obtained analytically, along with the depths of their weights, in terms of an integrity basis consisting of sets of compatible (or adjacent) weights, one from each fundamental orbit. The fundamental orbits and others of the same level and congruence class are then decomposed into irreducible representations (IR). Since the orbit →IR matrix is triangular, it will be easy to invert it to get orbit multiplicities and subalgebra branching rules.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529605
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  • 3
    Electronic Resource
    Electronic Resource
    Orbit–orbit branching rules between simple low-rank algebras and equal-rank subalgebras (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1618-1626 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Complete orbit–orbit branching rules, or equivalently, reduction of Weyl group orbits, between each simple algebra of rank 3 or less, and its equal-rank subalgebras and between F4 and each of its equal-rank subalgebras are given. The generic case An&supuline;An−1×U(1), the subjoining F4(approximately-greater-than)B3×U(1), and E8&supuline;E6×A2 (first and seventh highest weight labels nonzero) are also treated. Branching rules between rank 4 and 5 simple algebras and E6 and their equal-rank subalgebras are available in a depository.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529687
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  • 4
    Electronic Resource
    Electronic Resource
    The Demazure–Tits subgroup of a simple Lie group (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 777-796 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The Demazure–Tits subgroup of a simple Lie group G is the group of invariance of Clebsch–Gordan coefficients tables (assuming an appropriate choice of basis). The structure of the Demazure–Tits subgroups of An, Bn, Cn, Dn, and G2 is described. Orbits of the permutation action of the DT group in any irreducible finite-dimensional representation space of A2, C2, and G2 are decomposed into the sum of irreducible representations of the DT group.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527971
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  • 5
    Electronic Resource
    Electronic Resource
    Character states and generator matrix elements for Sp(4)⊃SU(2)×U(1) (1996)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 37 (1996), S. 3022-3031 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A new set of polynomial states (to be called character states) are derived for Sp(4) reduced to its SU(2)×U(1) subgroup, and the relevant generator matrix elements are evaluated for generic representations (a,b) of Sp(4). [The degenerate representations (a,0) and (0,b) were treated in our previous work and are also given in this paper]. The group–subgroup in question is that of the seniority model of nuclear physics. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.531691
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  • 6
    Electronic Resource
    Electronic Resource
    Collectivity and geometry. IV. Sp(6) &supuline; Sp(2)×O(3) basis states for open shells (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2995-2998 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Using generating function methods, branching rules for Sp(6) &supuline; Sp(2)×O(3) are derived. The branching rules suggest an integrity basis, or set of elementary permissible diagrams, in terms of which the subgroup basis states are defined; they correspond to vibrational, or Bohr–Mottelson type, states in the nuclear symplectic model.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.526674
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  • 7
    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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  • 8
    Electronic Resource
    Electronic Resource
    Polynomial tensors for the space groups pm and p4m (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 1534-1539 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Generating functions are calculated for polynomial tensors in the components of tensors of the one- and two-dimensional space groups pm and p4m. For tensors whose k vectors lie at rational points (denominator q) of the Brillouin zone, the problem is imaged by the corresponding problem for an appropriate finite group, and known methods are used for its solution. For tensors with continuous k the solution is obtained by letting q become infinite.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.526913
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  • 9
    Electronic Resource
    Electronic Resource
    A folk theorem revisited: Degenerate representations (1987)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 28 (1987), S. 1671-1672 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is known that when bases for generic irreducible representations of a semisimple group are reduced according to a semisimple subgroup the number of functionally independent missing label operators is just twice the number of missing labels. It is shown that the relation continues to hold when degenerate irreducible representations are considered.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527474
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  • 10
    Electronic Resource
    Electronic Resource
    Indices of representations of simple superalgebras (1987)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 28 (1987), S. 1673-1682 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Indices and anomaly numbers for representations of basic classical Lie superalgebras are defined, and their explicit expressions are derived in terms of Kac–Dynkin labels. Useful properties of indices and anomalies are determined, and several examples are given. A similar analysis is made for superindices and superanomalies, and it is demonstrated how all these objects form a helpful tool in decomposing tensor products or in constructing branching rules for representations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527475
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