The Gervais-Neveu-Felder equation for the Jordanian quasi-Hopf U_{h;y}(sl(2)) algebra

Using a contraction procedure, we construct a twist operator that satisfies a shifted cocycle condition, and leads to the Jordanian quasi-Hopf U_{h;y}(sl(2)) algebra. The corresponding universal ${\cal R}_{h}(y)$ matrix obeys a Gervais-Neveu-Felder equation associated with the U_{h;y}(sl(2)) algebra. For a class of representations, the dynamical Yang-Baxter equation may be expressed as a compatibility condition for the algebra of the Lax operators.Comment: Latex, 9 pages, no figure

Atypical Representations of Uq(sl(N))U_{q}(sl(N)) at Roots of Unity

We show how to adapt the Gelfand-Zetlin basis for describing the atypical representation of ${\cal U}_{\displaystyle{q}}(sl(N))$ when $q$ is root of unity. The explicit construction of atypical representation is presented in details for $N=3$.Comment: 18 pages, Tex-file and 2 figures. Uuencoded, compressed and tared archive of plain tex file and postscript figure file. Upon uudecoding, uncompressing and taring, tex the file atypique.te

Design of a "Digital Atlas Vme Electronics" (DAVE) Module

ATLAS-SCT has developed a new ATLAS trigger card, 'Digital Atlas Vme Electronics' ("DAVE"). The unit is designed to provide a versatile array of interface and logic resources, including a large FPGA. It interfaces to both VME bus and USB hosts. DAVE aims to provide exact ATLAS CTP (ATLAS Central Trigger Processor) functionality, with random trigger, simple and complex deadtime, ECR (Event Counter Reset), BCR (Bunch Counter Reset) etc. being generated to give exactly the same conditions in standalone running as experienced in combined runs. DAVE provides additional hardware and a large amount of free firmware resource to allow users to add or change functionality. The combination of the large number of individually programmable inputs and outputs in various formats, with very large external RAM and other components all connected to the FPGA, also makes DAVE a powerful and versatile FPGA utility cardComment: 8 pages, 4 figures, TWEPP-2011; E-mail: [email protected]

The fundamental invariant of the Hecke algebra Hn(q)H_n(q) characterizes the representations of Hn(q)H_n(q), SnS_n, SUq(N)SU_q(N) and SU(N)SU(N)

The irreducible representations (irreps) of the Hecke algebra $H_n(q)$ are shown to be completely characterized by the fundamental invariant of this algebra, $C_n$. This fundamental invariant is related to the quadratic Casimir operator, ${\cal{C}}_2$, of $SU_q(N)$, and reduces to the transposition class-sum, $[(2)]_n$, of $S_n$ when $q\rightarrow 1$. The projection operators constructed in terms of $C_n$ for the various irreps of $H_n(q)$ are well-behaved in the limit $q\rightarrow 1$, even when approaching degenerate eigenvalues of $[(2)]_n$. In the latter case, for which the irreps of $S_n$ are not fully characterized by the corresponding eigenvalue of the transposition class-sum, the limiting form of the projection operator constructed in terms of $C_n$ gives rise to factors that depend on higher class-sums of $S_n$, which effect the desired characterization. Expanding this limiting form of the projection operator into a linear combination of class-sums of $S_n$, the coefficients constitute the corresponding row in the character table of $S_n$. The properties of the fundamental invariant are used to formulate a simple and efficient recursive procedure for the evaluation of the traces of the Hecke algebra. The closely related quadratic Casimir operator of $SU_q(N)$ plays a similar role, providing a complete characterization of the irreps of $SU_q(N)$ and - by constructing appropriate projection operators and then taking the $q\rightarrow 1$ limit - those of $SU(N)$ as well, even when the quadratic Casimir operator of the latter does not suffice to specify its irreps.Comment: 32 pages, Latex-file, Tables in a Latex form are included at the end of the fil

On Auxiliary Fields in BF Theories

We discuss the structure of auxiliary fields for non-Abelian BF theories in arbitrary dimensions. By modifying the classical BRST operator, we build the on-shell invariant complete quantum action. Therefore, we introduce the auxiliary fields which close the BRST algebra and lead to the invariant extension of the classical action.Comment: 7 pages, minor changes, typos in equations corrected and acknowledgements adde

A Physicist's Proof of the Lagrange-Good Multivariable Inversion Formula

We provide yet another proof of the classical Lagrange-Good multivariable inversion formula using techniques of quantum field theory.Comment: 9 pages, 3 diagram

Pedestrian lane detection for assistive navigation of blind people

Navigating safely in outdoor environments is a challenging activity for vision-impaired people. This paper is a step towards developing an assistive navigation system for the blind. We propose a robust method for detecting the pedestrian marked lanes at traffic junctions. The proposed method includes two stages: regions of interest (ROI) extraction and lane marker verification. The ROI extraction is performed by using colour and intensity information. A probabilistic framework employing multiple geometric cues is then used to verify the extracted ROI. The experimental results have shown that the proposed method is robust under challenging illumination conditions and obtains superior performance compared to the existing methods. © 2012 ICPR Org Committee

Determinant Bounds and the Matsubara UV Problem of Many-Fermion Systems

It is known that perturbation theory converges in fermionic field theory at weak coupling if the interaction and the covariance are summable and if certain determinants arising in the expansion can be bounded efficiently, e.g. if the covariance admits a Gram representation with a finite Gram constant. The covariances of the standard many--fermion systems do not fall into this class due to the slow decay of the covariance at large Matsubara frequency, giving rise to a UV problem in the integration over degrees of freedom with Matsubara frequencies larger than some Omega (usually the first step in a multiscale analysis). We show that these covariances do not have Gram representations on any separable Hilbert space. We then prove a general bound for determinants associated to chronological products which is stronger than the usual Gram bound and which applies to the many--fermion case. This allows us to prove convergence of the first integration step in a rather easy way, for a short--range interaction which can be arbitrarily strong, provided Omega is chosen large enough. Moreover, we give - for the first time - nonperturbative bounds on all scales for the case of scale decompositions of the propagator which do not impose cutoffs on the Matsubara frequency.Comment: 29 pages LaTe