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  • 1
    Electronic Resource
    Electronic Resource
    Cohomology in connection space, family index theorem, and Abelian gauge structure (1987)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 28 (1987), S. 1709-1715 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Using the natural connection form on a principal bundle P(M,G) and the bundle @FA(@FA/G,G) a systematic derivation of the double-cohomological series constituted by the exterior differential d on space-time M and arbitrary, horizontal, and vertical variations in connection space is given. The relationship between these cohomologies and the family index theorem is clarified. The formalism is then used to analyze Abelian gauge structure inside non-Abelian gauge theory. The pertinent functional U(1) connection form, curvature form, and three-form "curvature'' are identified and computed, and are related to the θ vacuum, anomalous commutation relation, and Jacobi identity, respectively. Some of the results differ from those obtained by Wu and Zee [Nucl. Phys. B 258, 157 (1985)] and Niemi and Semenoff [Phys. Rev. Lett. 55, 227 (1985)] and the results of this paperrecover theirs under certain conditions. Finally the generalization of the formalism to a nontrivial principal bundle by introduction of a fixed background connection form is discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527480
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  • 2
    Electronic Resource
    Electronic Resource
    Casimir invariants from quasi-Hopf (super)algebras (2000)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 41 (2000), S. 547-568 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We show how to construct, starting from a quasi-Hopf (super)algebra, central elements or Casimir invariants. We show that these central elements are invariant under quasi-Hopf twistings. As a consequence, the elliptic quantum (super)groups, which arise from twisting the normal quantum (super)groups, have the same Casimir invariants as the corresponding quantum (super)groups. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.533151
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  • 3
    Electronic Resource
    Electronic Resource
    Type-I quantum superalgebras, q-supertrace, and two-variable link polynomials (1996)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 37 (1996), S. 987-1003 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A new general eigenvalue formula for the eigenvalues of Casimir invariants, for the type-I quantum superalgebras, is applied to the construction of link polynomials associated with any finite dimensional unitary irrep for these algebras. This affords a systematic construction of new two-variable link polynomials associated with any finite dimensional irrep (with a real highest weight) for the type-I quantum superalgebras. In particular infinite families of nonequivalent two-variable link polynomials are determined in fully explicit form. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.531422
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  • 4
    Electronic Resource
    Electronic Resource
    Quantum affine Lie algebras, Casimir invariants, and diagonalization of the braid generator (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 6757-6773 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Let Uq(Gˆ) be an infinite-dimensional quantum affine Lie algebra. A family of central elements or Casimir invariants are constructed and their eigenvalues computed in any integrable irreducible highest weight representation. These eigenvalue formulas are shown to be absolutely convergent when the deformation parameter q is such that ||q||(approximately-greater-than)1. It is proven that the universal R-matrix R of Uq(Gˆ) satisfies the celebrated conjugation relation R°=TR with T the usual twist map. As applications, the braid generator is shown to be diagonalizable on arbitrary tensor product modules of integrable irreducible highest weight Uq(Gˆ)-module and a spectral decomposition formula for the braid generator is obtained which is the generalization of Reshetikhin's and Gould's forms to the present affine case. Casimir invariants acting on a specified module are also constructed and their eigenvalues, again absolutely convergent for ||q||(approximately-greater-than)1, computed by means of the spectral decomposition formula. © 1994 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530641
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  • 5
    Electronic Resource
    Electronic Resource
    Uq[sl(2|&dbgcaret;1)] vertex operators, screen currents, and correlation functions at an arbitrary level (2000)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 41 (2000), S. 5277-5291 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Bosonized q-vertex operators related to the four-dimensional evaluation modules of the quantum affine superalgebra Uq[sl(2|&dbgcaret;1)] are constructed for arbitrary level k=α, where α≠0,−1 is a complex parameter appearing in the four-dimensional evaluation representations. They are intertwiners among the level-α highest weight Fock–Wakimoto modules. Screen currents which commute with the action of Uq[sl(2|&dbgcaret;1)] up to total differences are presented. Integral formulas for N-point functions of type I and type II q-vertex operators are proposed. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.533409
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  • 6
    Electronic Resource
    Electronic Resource
    Quasispin graded-fermion formalism and gl(m|n)↓osp(m|n) branching rules (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 5371-5386 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The graded-fermion algebra and quasispin formalism are introduced and applied to obtain the gl(m|n)↓osp(m|n) branching rules for the "two-column" tensor irreducible representations of gl(m|n), for the case m≤n(n〉2). In the case m〈n, all such irreducible representations of gl(m|n) are shown to be completely reducible as representations of osp(m|n). This is also shown to be true for the case m=n, except for the "spin-singlet" representations, which contain an indecomposable representation of osp(m|n) with composition length 3. These branching rules are given in fully explicit form. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.533075
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  • 7
    Electronic Resource
    Electronic Resource
    Level-one representations and vertex operators of quantum affine superalgebra Uq[gl(N(circumflex)|N)] (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 6110-6124 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Level-one representations of the quantum affine superalgebra Uq[gl(N(circumflex)|N)] associated with the appropriate nonstandard system of simple roots and q-vertex operators (intertwining operators) associated with the level-one modules are constructed explicitly in terms of free bosonic fields. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.533073
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  • 8
    Electronic Resource
    Electronic Resource
    Quasi-Hopf superalgebras and elliptic quantum supergroups (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 5264-5282 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We introduce the quasi-Hopf superalgebras which are Z2-graded versions of Drinfeld's quasi-Hopf algebras. We describe the realization of elliptic quantum supergroups as quasi-triangular quasi-Hopf superalgebras obtained from twisting the normal quantum supergroups by twistors which satisfy the graded shifted cocycle condition, thus generalizing the quasi-Hopf twisting procedure to the supersymmetric case. Two types of elliptic quantum supergroups are defined, that is, the face type Bq,λ(G) and the vertex type Aq,p[sl(n|&dbgcaret;n)] (and Aq,p[gl(n|&dbgcaret;n)]), where G is any Kac–Moody superalgebra with symmetrizable generalized Cartan matrix. It appears that the vertex type twistor can be constructed only for Uq[sl(n|&dbgcaret;n) in a nonstandard system of simple roots, all of which are fermionic. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.533029
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  • 9
    Electronic Resource
    Electronic Resource
    The Virasoro algebra and group in four dimensions (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1241-1243 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The Virasoro algebra and group are examined in (3+1)-dimensional theory with an Abelian gauge field coupled with the gravitational field. The two-cocycle for the group is constructed by using the so-called descent equation. Its infinitesimal version gives the Schwinger–Jackiw–Johnson term in the Virasoro algebra in 3+1 dimensions. It appears that in the case of an external monopole field the Virasoro algebra and group in 3+1 dimensions are the direct generalization of the standard ones in 1+1 dimensions, respectively.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528199
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  • 10
    Electronic Resource
    Electronic Resource
    On Super-RS Algebra and Drinfeld Realization of Quantum Affine Superalgebras (1998)
    Springer
    Letters in mathematical physics 44 (1998), S. 291-308 
    Details
    ISSN: 1573-0530
    Keywords: Super-RS algebra ; Drinfeld realization ; quantum affine superalgebras.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We describe the realization of the super-Reshetikhin–Semenov-Tian-Shansky (RS) algebra in quantum affine superalgebras, thus generalizing the approach of Frenkel and Reshetikhin to the supersymmetric (and twisted) case. The algebraic homomorphism between the super-RS algebra and the Drinfeld current realization of quantum affine superalgebras is established by using the Gauss decomposition technique of Ding and Frenkel. As an application, we obtain Drinfeld realization of quantum affine superalgebra Uq [osp(1|2)(1)] and its degeneration – central extended super-Yangian double DYħ [osp(1∣2)(1)].
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1007494602290
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