70 research outputs found

    Theta functions for lattices of SU(3) hyper-roots

    Full text link
    We recall the definition of the hyper-roots that can be associated to modules-categories over the fusion categories defined by the choice of a simple Lie group G together with a positive integer k. This definition was proposed in 2000, using another language, by Adrian Ocneanu. If G=SU(2), the obtained hyper-roots coincide with the usual roots for ADE Dynkin diagrams. We consider the associated lattices when G=SU(3) and determine their theta functions in a number of cases; these functions can be expressed as modular forms twisted by appropriate Dirichlet characters.Comment: 33 pages, 9 figure

    Character tables (modular data) for Drinfeld doubles of finite groups

    Full text link
    In view of applications to conformal field theory or to other branches of theoretical physics and mathematics, new examples of character tables for Drinfeld doubles of finite groups (modular data) are made available on a website.Comment: 7 pages, 1 figure, 7th International Conference on Mathematical Methods in Physics, Rio de Janeiro, Brazil, April 2012. Version 2: a misleading sentence was removed from section 2. http://pos.sissa.it/archive/conferences/175/024/ICMP%202012_024.pd

    Global dimensions for Lie groups at level k and their conformally exceptional quantum subgroups

    Full text link
    We obtain formulae giving global dimensions for fusion categories defined by Lie groups G at level k and for the associated module-categories obtained via conformal embeddings. The results can be expressed in terms of Lie quantum superfactorials of type G. The later are related, for the type Ar, to the quantum Barnes function.Comment: 20 pages, talk given at: Coloquio de Algebras de Hopf, Grupos Cuanticos y Categorias Tensoriales, Cordoba, Argentina, 200

    Quantum McKay correspondence and global dimensions for fusion and module-categories associated with Lie groups

    Full text link
    Global dimensions for fusion categories defined by a pair (G,k), where G is a Lie group and k a positive integer, are expressed in terms of Lie quantum superfactorial functions. The global dimension is defined as the square sum of quantum dimensions of simple objects, for the category of integrable modules over an affine Lie algebra at some level. The same quantities can also be defined from the theory of quantum groups at roots of unity or from conformal field theory WZW models. Similar results are also presented for those associated module-categories that can be obtained via conformal embeddings (they are "quantum subgroups" of a particular kind). As a side result, we express the classical (or quantum) Weyl denominator of simple Lie groups in terms of products of classical (or quantum) factorials calculated for the exponents of the group. Some calculations use the correspondence existing between periodic quivers for simply-laced Lie groups and fusion rules for module-categories (alias nimreps) of type SU(2).Comment: 23 pages. Improvements suggested by a referee: those parts that had much overlap with previous work of the author have been removed, the section discussing the relation between SU2 fusion numbers and roots and weights of Lie groups was enlarged, new reference [9], new appendi

    Clifford algebras, spinors and fundamental interactions : Twenty Years After

    Full text link
    This is a short review of the algebraic properties of Clifford algebras and spinors. Their use in the description of fundamental physics (elementary particles) is also summarized. Lecture given at the ICCA7 conference, Toulouse (23/05/2005)Comment: 14 page

    On quantum symmetries of ADE graphs

    Full text link
    The double triangle algebra(DTA) associated to an ADE graph is considered. A description of its bialgebra structure based on a reconstruction approach is given. This approach takes as initial data the representation theory of the DTA as given by Ocneanu's cell calculus. It is also proved that the resulting DTA has the structure of a weak *-Hopf algebra. As an illustrative example, the case of the graph A3 is described in detail.Comment: 15 page

    Large scale geometry and evolution of a universe with radiation pressure and cosmological constant

    Get PDF
    In view of new experimental results that strongly suggest a non-zero cosmological constant, it becomes interesting to revisit the Friedman-Lemaitre model of evolution of a universe with cosmological constant and radiation pressure. In this paper, we discuss the explicit solutions for that model and perform numerical explorations for reasonable values of cosmological parameters. We also analyse the behaviour of redshifts in such models and the description of ``very large scale geometrical features'' when analysed by distant observers.Comment: 31 pages, Latex, 9 eps figures. Revised version: Introduction was extended and we have added an application to cosmology of the duplication formula for the elliptic Weierstrass P functio

    From orbital measures to Littlewood-Richardson coefficients and hive polytopes

    Full text link
    The volume of the hive polytope (or polytope of honeycombs) associated with a Littlewood- Richardson coefficient of SU(n), or with a given admissible triple of highest weights, is expressed, in the generic case, in terms of the Fourier transform of a convolution product of orbital measures. Several properties of this function -- a function of three non-necessarily integral weights or of three multiplets of real eigenvalues for the associated Horn problem-- are already known. In the integral case it can be thought of as a semi-classical approximation of Littlewood-Richardson coefficients. We prove that it may be expressed as a local average of a finite number of such coefficients. We also relate this function to the Littlewood-Richardson polynomials (stretching polynomials) i.e., to the Ehrhart polynomials of the relevant hive polytopes. Several SU(n) examples, for n=2,3,...,6, are explicitly worked out.Comment: 32 pages, 4 figures. This version (V4): a few corrected typo

    Conjugation properties of tensor product multiplicities

    Full text link
    It was recently proven that the total multiplicity in the decomposition into irreducibles of the tensor product lambda x mu of two irreducible representations of a simple Lie algebra is invariant under conjugation of one of them; at a given level, this also applies to the fusion multiplicities of affine algebras. Here, we show that, in the case of SU(3), the lists of multiplicities, in the tensor products lambda x mu and lambda x bar{mu}, are identical up to permutations. This latter property does not hold in general for other Lie algebras. We conjecture that the same property should hold for the fusion product of the affine algebra of su(3) at finite levels, but this is not investigated in the present paper.Comment: 29 pages, 23 figures. v2: Added references. Corrected typos. Some more explanations and comments have been added : subsections 1.4, 4.2.4 and a last paragraph in section 3.3. To appear in J Phys
    • …
    corecore