Coherent State Construction of Representations of osp(2|2) and Primary Fields of osp(2|2) Conformal Field Theory

Representations of the superalgebra $osp(2|2)$ and current superalgebra $osp(2|2)^{(1)}_k$ in the standard basis are investigated. All finite-dimensional typical and atypical representations of $osp(2|2)$ are constructed by the vector coherent state method. Primary fields of the non-unitary conformal field theory associated with $osp(2|2)^{(1)}_k$ in the standard basis are constructed for arbitrary level $k$.Comment: 12 pages, cosmetic changes, to appear in Phys. Lett.

Cayley-Klein contractions of orthosymplectic superalgebras

We define a class of orthosymplectic superalgebras $osp(m;j|2n;\omega)$ which may be obtained from $osp(m|2n)$ by contractions and analytic continuations in a similar way as the orthogonal and the symplectic Cayley-Klein algebras are obtained from the corresponding classical ones. Contractions of $osp(1|2)$ and $osp(3|2)$ are regarded as an examples.Comment: 6 pages, Latex. Report given at 2 Int. Symposium "Quantum Theory and Symmetry", 18-21 July, 2001, Krakow (Poland

Conformal symmetries of the super Dirac operator

In this paper, the Dirac operator, acting on super functions with values in super spinor space, is defined along the lines of the construction of generalized Cauchy-Riemann operators by Stein and Weiss. The introduction of the superalgebra of symmetries osp(m|2n) is a new and essential feature in this approach. This algebra of symmetries is extended to the algebra of conformal symmetries osp(m + 1, 1|2n). The kernel of the Dirac operator is studied as a representation of both algebras. The construction also gives an explicit realization of the Howe dual pair osp(1|2) x osp(m|2n) \subset osp(m + 4n|2m + 2n). Finally, the super Dirac operator gives insight into the open problem of classifying invariant first order differential operators in super parabolic geometries

The algebraic Bethe ansatz for rational braid-monoid lattice models

In this paper we study isotropic integrable systems based on the braid-monoid algebra. These systems constitute a large family of rational multistate vertex models and are realized in terms of the B_n, C_n and D_n Lie algebra and by the superalgebra Osp(n|2m). We present a unified formulation of the quantum inverse scattering method for many of these lattice models. The appropriate fundamental commutation rules are found, allowing us to construct the eigenvectors and the eigenvalues of the transfer matrix associated to the B_n, C_n, D_n, Osp(2n-1|2), Osp(2|2n-2), Osp(2n-2|2) and Osp(1|2n) models. The corresponding Bethe Ansatz equations can be formulated in terms of the root structure of the underlying algebra.Comment: plain latex, 48 pages, 1 figure (under request

Central extensions of generalized orthosymplectic Lie superalgebras

The key ingredient of this paper is the universal central extension of the generalized orthosymplectic Lie superalgebra $\mathfrak{osp}_{m|2n}(R,{}^-)$ coordinatized by a unital associative superalgebra $(R,{}^-)$ with superinvolution. Such a universal central extension will be constructed via a Steinberg orthosymplectic Lie superalgebra coordinated by $(R,{}^-)$. The research on the universal central extension of $\mathfrak{osp}_{m|2n}(R,{}^-)$ will yield an identification between the second homology group of the generalized orthosymplectic Lie superalgebra $\mathfrak{osp}_{m|2n}(R,{}^-)$ and the first $\mathbb{Z}/2\mathbb{Z}$-graded skew-dihedral homology group of $(R,{}^-)$ for $(m,n)\neq(2,1),(1,1)$. The universal central extensions of $\mathfrak{osp}_{2|2}(R,{}^-)$ and $\mathfrak{osp}_{1|2}(R,{}^-)$ will also be treated separately.Comment: The decomposition of $\mathfrak{osp}_{m|2n}(R,{}^-)$ given after the proof of Proposition 3.2 has been revised. Accordingly, the decomposition of $\mathfrak{sto}_{m|2n}(R,{}^-)$ in Proposition 3.6 and 4.1 has been revised. A few typos have been fixe

Fast and Accurate Random Walk with Restart on Dynamic Graphs with Guarantees

Given a time-evolving graph, how can we track similarity between nodes in a fast and accurate way, with theoretical guarantees on the convergence and the error? Random Walk with Restart (RWR) is a popular measure to estimate the similarity between nodes and has been exploited in numerous applications. Many real-world graphs are dynamic with frequent insertion/deletion of edges; thus, tracking RWR scores on dynamic graphs in an efficient way has aroused much interest among data mining researchers. Recently, dynamic RWR models based on the propagation of scores across a given graph have been proposed, and have succeeded in outperforming previous other approaches to compute RWR dynamically. However, those models fail to guarantee exactness and convergence time for updating RWR in a generalized form. In this paper, we propose OSP, a fast and accurate algorithm for computing dynamic RWR with insertion/deletion of nodes/edges in a directed/undirected graph. When the graph is updated, OSP first calculates offset scores around the modified edges, propagates the offset scores across the updated graph, and then merges them with the current RWR scores to get updated RWR scores. We prove the exactness of OSP and introduce OSP-T, a version of OSP which regulates a trade-off between accuracy and computation time by using error tolerance {\epsilon}. Given restart probability c, OSP-T guarantees to return RWR scores with O ({\epsilon} /c ) error in O (log ({\epsilon}/2)/log(1-c)) iterations. Through extensive experiments, we show that OSP tracks RWR exactly up to 4605x faster than existing static RWR method on dynamic graphs, and OSP-T requires up to 15x less time with 730x lower L1 norm error and 3.3x lower rank error than other state-of-the-art dynamic RWR methods.Comment: 10 pages, 8 figure

Topological String on OSP(1|2)/U(1)

We propose an equivalence between topological string on OSP(1|2)/U(1) and \hat{c} \leq 1 superstring with N=1 world-sheet supersymmetry. We examine this by employing a free field representation of OSP(1|2) WZNW model and find an agreement on the spectrum. We also analyze this proposal at the level of scattering amplitudes by applying a map between correlation functions of OSP(1|2) WZNW model and those of N=1 Liouville theory.Comment: 25 pages, refereces adde