On Casimir's Ghost

We define on the universal enveloping superalgebra of osp(1|2n) a nonstandard adjoint action, endowing it with a module structure. This allows, in particular, to construct a bosonic operator which anticommutes with all the fermionic generators and which appears to be the square root of a certain Casimir operator.Comment: LaTeX2e, 13 pages,also available at http://lapphp0.in2p3.fr/preplapp/psth/ENSLAPP587.ps.gz ; one sentence removed and a note added. Not a major revisio

Remote Data Acquisition for SPS 352 MHz Superconducting Cavities

The SPS Machine is equipped with four SuperConducting (SC) Cavities. These are used to accelerate the beams during the electron and positron cycles of LEP. During the last two years the control system for these cavities has been upgraded to the LEP standard environment but, as the diagnostic capabilities were not sufficient to ensure their reliable operation, it was decided to build a Data Acquisition system based on commercial products. The present system is based on National Instrument PXI (an extension to CompactPCI for instrumentation) with 166 MHz Pentium running Windows NT and Labview5.1. In order to meet the user requirements, in terms of portability and speed, a client/server approach has been used. The Server can acquire 16 signals at a rate of 1 ms during the whole SPS supercycle. The Client is composed of a virtual oscilloscope interface (one or four channels) with on-line signal and timing selections and automatic data and user setting storage capabilities. The Client can run on the two platforms used at CERN (PC and HP/UX)

Super Yangian Y(osp(1|2)) and the Universal R-matrix of its Quantum Double

We present the Drinfel'd realisation of the super Yangian Y(osp(1|2)), including the explicit expression for the coproduct. We show in particular that it is necessary to introduce supplementary Serre relations. The construction of its quantum double is carried out. This allows us to give the universal R-matrix of DY(osp(1|2)).Comment: Latex2e, 21 page

Classical and Quantum sl(1|2) Superalgebras, Casimir Operators and Quantum Chain Hamiltonians

We examine the two parameter deformed superalgebra $U_{qs}(sl(1|2))$ and use the results in the construction of quantum chain Hamiltonians. This study is done both in the framework of the Serre presentation and in the $R$-matrix scheme of Faddeev, Reshetikhin and Takhtajan (FRT). We show that there exists an infinite number of Casimir operators, indexed by integers $p > 1$ in the undeformed case and by $p \in Z$ in the deformed case, which obey quadratic relations. The construction of the dual superalgebra of functions on $SL_{qs}(1|2)$ is also given and higher tensor product representations are discussed. Finally, we construct quantum chain Hamiltonians based on the Casimir operators. In the deformed case we find two Hamiltonians which describe deformed $t-J$ models.Comment: 27 pages, LaTeX, one reference moved and one formula adde

On the Quasi-Hopf structure of deformed double Yangians

We construct universal twists connecting the centrally extended double Yangian DY(sl(2))_c with deformed double Yangians DY_r(sl(2))_c, thereby establishing the quasi-Hopf structures of the latter.Comment: 11 page

Sugawara and vertex operator constructions for deformed Virasoro algebras

From the defining exchange relations of the A_{q,p}(gl_{N}) elliptic quantum algebra, we construct subalgebras which can be characterized as q-deformed W_N algebras. The consistency conditions relating the parameters p,q,N and the central charge c are shown to be related to the singularity structure of the functional coefficients defining the exchange relations of specific vertex operators representations of A_{q,p}({gl_{N}) available when N=2.Comment: 23 page

Control of total voltage in the large distributed RF system of LEP

The LEP RF system is made up of a large number of independent RF units situated around the ring near the interaction points. These have different available RF voltages depending on their type and they may be inactive or unable to provide full voltage for certain periods. The original RF voltage control system was based on local RF unit voltage function generators pre-loaded with individual tables for energy ramping. This was replaced this year by a more flexible global RF voltage control system. A central controller in the main control room has direct access to the units over the LEP TDM system via multiplexers and local serial links. It continuously checks the state of all the units and adjusts their voltages to maintain the desired total voltage under all conditions. This voltage is distributed among the individual units to reduce the adverse effects of RF voltage asymmetry around the machine as far as possible. The central controller is a VME system with 68040 CPU and real time multitasking operating system. Event driven communication handlers allow fast reliable concurrent data communication with the remote units. The RF unit low level RF G64 equipment controllers use a VME 68030 CPU to achieve the necessary response time and reliability

Integrable XYZ Model with Staggered Anisotropy Parameter

We apply to the XYZ model the technique of construction of integrable models with staggered parameters, presented recently for the XXZ case. The solution of modified Yang-Baxter equations is found and the corresponding integrable zig-zag ladder Hamiltonian is calculated. The result is coinciding with the XXZ case in the appropriate limit.Comment: 8 pages ; epic packag

Duality and Representations for New Exotic Bialgebras

We find the exotic matrix bialgebras which correspond to the two non-triangular nonsingular 4x4 R-matrices in the classification of Hietarinta, namely, R_{S0,3} and R_{S1,4}. We find two new exotic bialgebras S03 and S14 which are not deformations of the of the classical algebras of functions on GL(2) or GL(1|1). With this we finalize the classification of the matrix bialgebras which unital associative algebras generated by four elements. We also find the corresponding dual bialgebras of these new exotic bialgebras and study their representation theory in detail. We also discuss in detail a special case of R_{S1,4} in which the corresponding algebra turns out to be a special case of the two-parameter quantum group deformation GL_{p,q}(2).Comment: 33 pages, LaTeX2e, using packages: cite,amsfonts,amsmath,subeqn; reference updated; v3: corrections in subsection 3.