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Murphy, T.C.
Wisconsin Univ., Madison (USA)1981
Wisconsin Univ., Madison (USA)1981
AbstractAbstract
[en] Shift operators are constructed in product form for the Lie algebra O(p,q). Their normalization is found and they are used to construct discrete series representations of the algebra. Certain other representations are also constructed for the case q = 1
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1981; 113 p; University Microfilms Order No. 81-23,218; Thesis (Ph. D.).
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Report
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Thesis/Dissertation
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[en] Eigenvalues of the invariant operators of the orthogonal and symplectic groups have been obtained in closed form. All semisimple Lie groups, the unitary, orthogonal, and symplectic groups, are treated in a systematic way by modifying Perelomov and Popov's method. The eigenvalues of the invariant operators for the orthogonal and symplectic groups are then calculated with reference to the unitary group. (U.S.)
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Journal Article
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J. Math. Phys. (N.Y.); v. 16(6); p. 1239-1243
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Klimek, M.; Lukierski, J.
Funding organisation: Polish State Committee for Scientific Research, Warsaw (Poland)1995
Funding organisation: Polish State Committee for Scientific Research, Warsaw (Poland)1995
AbstractAbstract
[en] We describe the generators of κ-conformal transformations, leaving invariant the κ-deformed d'Alembert equation. In such a way one obtains the conformal extension of-shell spin spin zero realization of κ-deformed Poincare algebra. Finally the algebraic structure of κ-deformed conformal algebra is discussed. (author)
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KBN GRANT NO 2P30208706; 23 refs.
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[en] In the same way the folding of the Dynkin diagram of A2n (respectively A2n+1) produces the Bn (respectively Cn) Dynkin diagram, the symmetry algebra W of a Toda model based on Bn (respectively Cn) can be seen as resulting from the folding of a W-algebra based on A2n (respectively A2n-1). More generally, W algebras related to the B-C-D algebra series can appear from W algebras related to the unitary ones. Such an approach is in particular well adapted to obtain fusion rules of W algebras based on non simply laced algebras from fusion rules corresponding to the An case. Analogously, super W algebras associated to orthosymplectic superalgebras are deduced from those relative to the unitary A(m, n) series. (orig.)
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Izmest'ev, A.A.; Pogosyan, G.S.; Sisakyan, A.N.; Winternitz, P.
Bogolyubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna (Russian Federation)1999
Bogolyubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna (Russian Federation)1999
AbstractAbstract
[en] Lie algebra contractions from o(n + 1) to e(n) are used to obtain asymptotic limits of interbases expansions between bases corresponding to different subgroup chains for the group O(n + 1). The contractions lead to interbases expansions for different subgroup chains of the Euclidean group E(n). The article is restricted to the low dimensional cases n = 2 and n = 3
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1999; 16 p; 21 refs., 4 figs. Submitted to Journal of Physics. A, Mathematical and General
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Report
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Poghosyan, V S; Priezzhev, V B, E-mail: vpoghos@theor.jinr.ru, E-mail: priezzvb@theor.jinr.ru2013
AbstractAbstract
[en] The two-dimensional dense O(n) loop model for n = 1 is equivalent to the bond percolation and for n = 0 to the dense polymers or spanning trees. We consider the boundary correlations on the half space and calculate the probability Pb that a cluster of bonds has a single common point with the boundary. In the limit n → 0, we find an analytical expression for Pb using the generalized Kirchhoff theorem. (paper)
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Available from http://dx.doi.org/10.1088/1751-8113/46/14/145002; Country of input: International Atomic Energy Agency (IAEA)
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Journal Article
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Journal of Physics. A, Mathematical and Theoretical (Online); ISSN 1751-8121;
; v. 46(14); [18 p.]

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Bourgine, Jean-Emile; Hosomichi, Kazuo, E-mail: hosomiti@kias.re.kr2009
AbstractAbstract
[en] We study the new boundary condition of the O(n) model proposed by Jacobsen and Saleur using the matrix model. The spectrum of boundary operators and their conformal weights are obtained by solving the loop equations. Using the diagrammatic expansion of the matrix model as well as the loop equations, we make an explicit correspondence between the new boundary condition of the O(n) model and the 'alternating height' boundary conditions in RSOS model.
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Available from http://dx.doi.org/10.1088/1126-6708/2009/01/009; Country of input: International Atomic Energy Agency (IAEA)
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Journal Article
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Journal of High Energy Physics; ISSN 1126-6708;
; v. 01(2009); p. 009

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[en] Suppose that q is not a root of unity. We classify all bicovariant differential calculi of dimension greater than one on the quantum groups GLq(N), Oq(N) and Spq(N) for which the differentials duij of the matrix entries uij generate the left module of first order forms. Our first classification theorem asserts that there are precisely two one-parameter families of such calculi on GLq(N) for N≥3. In the limit q → 1 only two of these calculi give the ordinary differential calculus on GL(N). Our second main theorem states that apart from finitely many q there exist precisely two differential calculi with these properties on Oq(N) and Spq(N) for N≥4. There are four such calculi on Oq(3). We introduce two new 4-dimensional bicovariant differential calculi on Oq(3). (orig.)
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[en] It is suggested that a dynamical space-time symmetry group of a given non-linear relativistic theory is able to generate an internal symmetry group. It is shown that only 0(2N-1,1) and 0(2N,1) groups are admitted as simple dynamical symmetry groups, and they imply U(2sup(N-2)) as the largest internal symmetry groups. The boson and fermion content of the considered models is determined and a new dynamical symmetry breaking mechanism, different from the spontaneous one, is introduced. (author)
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International symposium on selected topics in quantum field theory and mathematical physics; Bechyne (Czechoslovakia); 14-19 Jun 1981
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Journal Article
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Conference
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Czechoslovak Journal of Physics; ISSN 0011-4626;
; v. 32(6); p. 634-644

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AbstractAbstract
[en] A model is presented in two space dimensions which has an infinite number of kink and antikink solutions. The Lagrangian of the model is described in terms of three-real-valued scalar fields qsub(i)(x,t). The Lagrange multiplier lambda (x,t) introduces a self-interaction of the qsub(i)-fields by restricting the field vector q on the unit sphere. The Lagrangian of the model is vivariant under the action of the internal symmetry group O3
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Journal Article
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Lett. Nuovo Cim; v. 15(4); p. 97-100
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