On centralizer algebras for spin representations

We give a presentation of the centralizer algebras for tensor products of spinor representations of quantum groups via generators and relations. In the even-dimensional case, this can be described in terms of non-standard q-deformations of orthogonal Lie algebras; in the odd-dimensional case only a certain subalgebra will appear. In the classical case q = 1 the relations boil down to Lie algebra relations

On fusion algebra of chiral SU(N)kSU(N)_{k} models

We discuss some algebraic setting of chiral $SU(N)_{k}$ models in terms of the statistical dimensions of their fields. In particular, the conformal dimensions and the central charge of the chiral $SU(N)_{k}$ models are calculated from their braid matrices. Futhermore, at level K=2, we present the characteristic polynomials of their fusion matrices in a factored form.Comment: 11 pages, ioplpp

Topological Quantum Field Theories and Operator Algebras

We review "quantum" invariants of closed oriented 3-dimensional manifolds arising from operator algebras.Comment: For proceedings of "International Workshop on Quantum Field Theory and Noncommutative Geometry", Sendai, November 200

Staff Week as a Modernization Tool in Translator Training Programs: Experience of Cooperation in the Erasmus +

Translator training in the coordinates of the global educational space implies an integrative approach to unification and at the same time extension of theoretical, methodological and didactic approaches. At the same time, the search for effective ways and tools of interaction is carried out at different levels – academic, professional communities, individual persons, since the profession of a translator implies communication without borders, networking and constant expansion of the circle of partnerships. This article analyzes the effectiveness of one of the current tools for interuniversity cooperation in the format of Staff Week internships, integrated into the Erasmus + academic mobility program, in the focus of its validity and functionality in training translators. The study provides an analysis of domestic and foreign scientific and educational works on the scientific, didactic potential of the program, a review of the current state of affairs in the field of intercollegiate cooperation within Erasmus + on the example of the Russian university – Volgograd State University and the German university – International University SDI Munich. These universities have been developing partnership relations since the 90s, however, Erasmus has been cooperating with them recently and quite successfully. The material of the study is an overview of the structure and content of the Staff Week internships of Volgograd State University teachers at SDI Munich. The Intercultural component of interaction is effectively manifested in the optimization of didactic models in the partner university, updating of curricula, expanding the horizons of joint projects, which certainly contributes to improving the quality of educational services in the field of translation and promotes the integration of education in general. The results of this research can be useful for the organization of the educational process in university educational programs in the areas of training specialists in the field of translation and intercultural communication

Tritium in Metallen: Präparationstechnik (Tritiumlabor): Eigenschaften von Tritium in Vanadium, Niob, Tantal und Palladium

In order to study the behaviour of tritium in metals, an all metal apparatus has been built for the safe handling of 100 mg of tritium (1000 Ci). This amount of tritium, for example, can load 10 g Pd to a concentration of T/Pd = 0.37. Samples can be loaded with tritium in a defined way by changing the gas pressure and the temperature. A PDP-II computer controlled the experiments by measuring pressures, room and sam pie temperatures and by adjusting the power for heating the sample. The main results of our studies in palladium, vanadium, niobium and tantalum are as follows: For the first time the phase diagram of the palladium-tritium system has been determined up to high concentrations. At constant concentration and temperature the following inequali ties hold for the desorption pressure: $P_{T_2}$(x, T) > $P_{D_2}$ (x, T) > $P_{H_2}$ (x, T). This is a consequence of the larger decrease of the energy of the vibrational levels in the molecule in comparison to the ones in the palladium lattice under isotopic exchange. In the two phase region ($\alpha$+$\beta$) the following values of the disintegration enthalpy $\Delta$H and -entropy $\Delta$S using the van't Hoff equation In p = - $\Delta$H/RT + $\Delta$S/R were obtained: [...

A New Young Diagrammatic Method For Kronecker Products of O(n) and Sp(2m)

A new simple Young diagrammatic method for Kronecker products of O(n) and Sp(2m) is proposed based on representation theory of Brauer algebras. A general procedure for the decomposition of tensor products of representations for O(n) and Sp(2m) is outlined, which is similar to that for U(n) known as the Littlewood rules together with trace contractions from a Brauer algebra and some modification rules given by King.Comment: Latex, 11 pages, no figure

On Haagerup's list of potential principal graphs of subfactors

We show that any graph, in the sequence given by Haagerup in 1991 as that of candidates of principal graphs of subfactors, is not realized as a principal graph except for the smallest two. This settles the remaining case of a previous work of the first author.Comment: 19 page

Anomalous Scale Dimensions from Timelike Braiding

Using the previously gained insight about the particle/field relation in conformal quantum field theories which required interactions to be related to the existence of particle-like states associated with fields of anomalous scaling dimensions, we set out to construct a classification theory for the spectra of anomalous dimensions. Starting from the old observations on conformal superselection sectors related to the anomalous dimensions via the phases which appear in the spectral decomposition of the center of the conformal covering group $Z(\widetilde{SO(d,2)}),$ we explore the possibility of a timelike braiding structure consistent with the timelike ordering which refines and explains the central decomposition. We regard this as a preparatory step in a new construction attempt of interacting conformal quantum field theories in D=4 spacetime dimensions. Other ideas of constructions based on the $AdS_{5}$-$CQFT_{4}$ or the perturbative SYM approach in their relation to the present idea are briefly mentioned.Comment: completely revised, updated and shortened replacement, 24 pages tcilatex, 3 latexcad figure