hidden sl n symmetry in conformal field theories we prove that an irreducible representation of the virasoro algebra can be extracted from an irreducible representation space of thesl 2 current algebra by putting a constraint on the latter using the becchi rouet stora tyutin formalism thus there is asl 2 symmetry in the virasoro algebra but it is gauged and hidden this construction of the virasoro algebra is the quantum analogue of the hamiltonian reduction we then are naturally lead to consider a constrainedsl 2 wess zumino witten model this system is also related to quantum field theory of coadjoint orbit of the virasoro group based on this result we present a canonical derivation of thesl 2 current algebra in polyakov s theory of two dimensional gravity it is a manifestation of thesl 2 symmetry in conformal field theory hidden by the quantum hamiltonian reduction we also discuss the quantum hamiltonian reduction of thesl 2 current algebra and its relation to thew n algebra of zamolodchikov this makes it possible to define a natural generalization of the geometric action for thew n algebra despite its non lie algebraic nature

numerical taylor expansions for invariant manifolds we consider numerical computation of taylor expansions of invariant manifolds around equilibria of maps and flows these expansions are obtained by writing the corresponding functional equation in a number of points setting up a nonlinear system of equations and solving this system using a simplified newton s method this approach will avoid symbolic or explicit numerical differentiation the linear algebra issues of solving the resulting sylvester equations are studied in detail

on integrability of the yang baxter σ model we prove that the recently introduced yang baxter model can be considered as an integrable deformation of the principal chiral model we find also an explicit one to one map transforming every solution of the principal chiral model into a solution of the deformed model with the help of this map the standard procedure of the dressing of the principal chiral solutions can be directly transferred into the deformed yang baxter context

symplectic structure of the moduli space of flat connection on a riemann surface we consider the canonical symplectic structure on the moduli space of flat g connections on a riemann surface of genus g with a marked points for a being a semisimple lie algebra we obtain an explicit efficient formula for this symplectic form and prove

the quantum group structure of 2d gravity and minimal models i on the unit circle an infinite family of chiral operators is constructed whose exchange algebra is given by the universalr matrix of the quantum groupsl 2 q this establishes the precise connection between the chiral algebra of two dimensional gravity or minimal models and this quantum group the method is to relate the monodromy properties of the operator differential equations satisfied by the generalized vertex operators with the exchange algebra ofsl 2 q the formulae so derived which generalize an earlier particular case worked out by babelon are remarkably compact and may be entirely written in terms of q deformed factorials and binomial coefficients

on poisson actions of compact lie groups on symplectic manifolds let g p be a compact simple poisson lie group equipped with a poisson structure p and m omega be a symplectic manifold assume that m carries a poisson action of g p and there is an equivariant moment map in the sense of lu and weinstein which maps

from geometric quantization to conformal field theory investigation of 2d conformal field theory in terms of geometric quantization is given we quantize the so called model space of the compact lie group virasoro group and kac moody group in particular we give a geometrical interpretation of the virasoro discrete series and explain that this type of geometric quantization reproduces the chiral part of cft minimal models 2d gravity wznw theory in the appendix we discuss the relation between classical constant r matrices and this geometrical approach

beyond floating point un systeme numerique est propose pour l arithmetique d ordinateur basee sur des fonctions exponentielles iterees l avantage principal est d extirper le sous passement et le depassement de capacite mais il y a quelques autres avantages et ceux ci sont decrits et discutes

algorithms and codes for the macdonald function recent progress and comparisons the modified bessel function kiv x also known as the macdonald function finds application in the kontorovich lebedev integral transform when x and v are real and positive in this paper a comparison of three codes for computing this function is made these codes differ in algorithmic approach timing and regions of validity one of them can be tested independent of the other two through wronskian checks and therefore is used as a standard against which the others are compared

on non integrability of classical strings in p brane backgrounds we investigate the question of possible integrability of classical string motion in curved p brane backgrounds for example the d3 brane metric interpolates between the flat and the ads5 s5 regions in which string propagation is integrable we find that while the point like string geodesic equations are integrable the equations describing an extended string in the complete d3 brane geometry are not the same conclusion is reached for similar brane intersection backgrounds interpolating between flat space and adsk sk we consider in particular the case of the ns 5 brane fundamental string background to demonstrate non integrability we make a special pulsating string ansatz for which the string equations reduce to an effective one dimensional system expanding near this simple solution leads to a linear differential equation for small fluctuations that cannot be solved in quadratures implying non integrability of the original set of string equations

zeros of the macdonald function of complex order the z zeros of the modified bessel function of the third kind k n z also known as modified hankel function or macdonald function are considered for arbitrary complex values of the order n approximate expressions for the zeros applicable in the cases of very small or very large n are given the behaviour of the zeros for varying n or arg n obtained numerically is illustrated by means of some graphics

software needs in special functions abstract currently available software for special functions exhibits gaps and defects in comparison to the needs of moderm high performance scientific computing and also surprisingly in comparison to what could be constructed from current algorithms in this paper we expose some of these deficiencies and identify the related need for user oriented testing software

locating and computing in parallel all the simple roots of special functions using pvm an algorithm is proposed for locating and computing in parallel and with certainty all the simple roots of any twice continuously di0erentiable function in any speci1c interval to compute with certainty all the roots the proposed method is heavily based on the knowledge of the total number of roots within the given interval to obtain this information we use results from topological degree theory and in particular the kronecker picard approach this theory gives a formula for the computation of the total number of roots of a system of equations within a given region which can be computed in parallel with this tool in hand we construct a parallel procedure for the localization and isolation of all the roots by dividing the given region successively and applying the above formula to these subregions until the 1nal domains contain at the most one root the subregions with no roots are discarded while for the rest a modi1cation of the well known bisection method is employed for the computation of the contained root the new aspect of the present contribution is that the computation of the total number of zeros using the kronecker picard integral as well as the localization and computation of all the roots is performed in parallel using the parallel virtual machine pvm pvm is an integrated set of software tools and libraries that emulates a general purpose 7exible heterogeneous concurrent computing framework on interconnected computers of varied architectures the proposed algorithm has large granularity and low synchronization and is robust it has been implemented and tested and our experience is that it can massively compute with certainty all the roots in a certain interval performance information from massive computations related to a recently proposed conjecture due to elbert this issue j comput appl math 133 2001 65 83 is reported c 2001 elsevier science b v all rights reserved

fock representations of the affine lie algebra a 1 1 the aim of this note is to show that the affine lie algebraa1 1 has a natural family v of fock representations on the spacec xi yj i andj parametrized by v c2 by corresponding the highest weight of to each the parameter spacec2 forms a double cover of the weight spacec 0 c 1 with singularities at linear forms of level 2 this number is 1 times the dual coxeter number our results contain explicit realizations of irreducible non integrable highest wieghta1 1 modules for generic v

quantum groups and wznw models an explanation of the appearance of quantum groups in chiral wznw models is given invariance of the theory under quantum group action is discussed

harmonic maps into lie groups classical solutions of the chiral model on considere deux aspects de la structure algebrique de 7b m l espace des applications harmoniques d un domaine a 2 dimensions simplement connexe dans un groupe de lie reel g r la forme reelle d un groupe complexe g on construit une representation du groupe boucle 7b a s 1 g r sur 7b m correspondant a l algebre de lie de kacmoody des deformations infinitesimales on decrit l action sur 7b m et l action d un sous groupe sur l espace des applications harmoniques dans des gaussmanniens dans une seconde partie on se restreint a une theorie qui s applique seulement quand est un domaine riemannien a 2 dimensions simplement connexe et le groupe est g r u n

integrable coupled σ models a systematic procedure for constructing classical integrable field theories with arbitrarily many free parameters is outlined it is based on the recent interpretation of integrable field theories as realizations of affine gaudin models in this language one can associate integrable field theories with affine gaudin models having arbitrarily many sites we present the result of applying this general procedure to couple together an arbitrary number of principal chiral model fields on the same lie group each with a wess zumino term

the local structure of poisson manifolds varietes de poisson et applications decomposition structures de poisson lineaires approximation lineaire systemes hamiltoniens le probleme de linearisation groupes de fonction realisations et applications impulsion paires duales et groupes de jauge existence des realisations unicite des realisations les problemes des 3 corps restreints et autres exemples

classification of real three dimensional poisson lie groups all real three dimensional poisson lie pl groups are explicitly constructed and fully classified under group automorphisms by making use of their one to one correspondence with the complete classification of real three dimensional lie bialgebras given in gomez 2000 j math phys 41 4939 many of these 3d pl groups are non coboundary structures whose poisson brackets are given here for the first time casimir functions for all three dimensional pl groups are given and some features of several pl structures are commented

stable synchronised states of coupled tchebyscheff maps abstract coupled tchebyscheff maps have recently been introduced to explain parameters in the standard model of particle physics using the stochastic quantisation of parisi and wu this paper studies dynamical properties of these maps finding analytic expressions for a number of periodic states and determining their linear stability numerical evidence is given for nonlinear stability of some of these states and also the presence of exponentially slow dynamics for some ranges of the parameter these results indicate that a theory of particle physics based on coupled map lattices must specify strong physical arguments for any choice of initial conditions and explain how stochastic quantisation is obtained in the many stable parameter regions

multifractal analysis of nonhyperbolic coupled map lattices application to genomic sequences symbolic sequences generated by coupled map lattices cmls can be used to model the chaotic like structure of genomic sequences in this study it is shown that diffusively coupled chebyshev maps of order 4 corresponding to a shift of four symbols very closely reproduce the multifractal spectrum d q of human genomic sequences for coupling constant 0 35 0 01 if q 0 the presence of rare configurations causes deviations for q 0 which disappear if the rare event statistics of the cml is modified such rare configurations are known to play specific functional roles in genomic sequences serving as promoters or regulatory elements

an integrable deformation of the ads5 s5superstring the s matrix on the world sheet theory of the string in ads has previously been shown to admit a deformation where the symmetry algebra is replaced by the associated quantum group the case where q is real has been identified as a particular deformation of the green schwarz sigma model an interpretation of the case with q a root of unity has until now been lacking we show that the green schwarz sigma model admits a discrete deformation which can be viewed as a rather simple deformation of the gauged wzw model where the deformation parameter q is then a kth root of unity where k is the level the deformed theory has the same equations of motion as the green schwarz sigma model but has a different symplectic structure we show that the resulting theory is integrable and has just the right amount of kappa symmetries that appear as a remnant of the fermionic part of the original gauge symmetry this points to the existence of a fully consistent deformed string background

efficiently computing many roots of a function we present a new bisection based method for counting and computing roots of a function in a given interval our method is focused on very large problems i e instances with the number of roots of the order of hundreds the method draws its power from the fact that the roots are expected to be many and is able to discover a large percentage of them very efficiently its main advantage apart from its efficiency is the fact that it requires only the sign of the function at a certain point and not its actual value also its simplicity makes it a suitable preprocessing step for reducing the size of the problem prior to more robust but also more demanding methods the algorithm is accompanied by a probabilistic analysis of its behavior which shows that a simple existence criterion like bolzano s rule can be a powerful tool in the zerofinding process

decomposable representations and lagrangian submanifolds of moduli spaces associated to surface groups the importance of explicit examples of lagrangian submanifolds of moduli spaces is revealed by papers such as dostoglou and salamon ann of math 2 139 3 581 640 1994 and salamon proceedings of the international congress of mathematicians vol 1 2 zurich 1994 pp 526 536 birkhauser basel 1995 given a 3 manifold m with boundary m dostoglou and salamon use such examples to obtain a proof of the atiyah floer conjecture relating the symplectic floer homology of the representation space hom 1 m u u associated to an explicit pair of lagrangian submanifolds of this representation space and the instanton homology of the 3 manifold m in the present paper we construct a lagrangian submanifold of the space of representations mathcal m g l hom mathcal c pi g l u u of the fundamental group g lof a punctured riemann surface g l into an arbitrary compact connected lie group u this lagrangian submanifold is obtained as the fixed point set of an anti symplectic involution hat beta defined on mathcal m g l we show that the involution hat beta is induced by a form reversing involution defined on the quasi hamiltonian space u times u g times mathcal c 1 times cdots times mathcal c l the fact that hat beta has a non empty fixed point set is a consequence of the real convexity theorem for group valued momentum maps proved in schaffhauser a real convexity theorem for quasi hamiltonian actions submitted 25 p 2007 http arxiv org abs math 0705 0858 the notion of decomposable representation provides a geometric interpretation of the lagrangian submanifold thus obtained

fock representations and brst cohomology insl 2 current algebra we investigate the structure of the fock modules overa 1 1 introduced by wakimoto we show that irreducible highest weight modules arise as degree zero cohomology groups in a brst like complex of fock modules chiral primary fields are constructed as brst invariant operators acting on fock modules as a result we obtain a free field representation of correlation functions of thesu 2 wzw model on the plane and on the torus we also consider representations of fractional level arising in polyakov s 2d quantum gravity finally we give a geometrical borel weil like interpretation of the wakimoto construction

symplectic structures associated to lie poisson groups the lie poisson analogues of the cotangent bundle and coadjoint orbits of a lie group are considered for the natural poisson brackets the symplectic leaves in these manifolds are classified and the corresponding symplectic forms are described thus the construction of the kirillov symplectic form is generalized for lie poisson groups

generalized type iib supergravity equations and non abelian classical r matrices we study yang baxter deformations of the ads superstring with non abelian classical r matrices which satisfy the homogeneous classical yang baxter equation by performing a supercoset construction we can get deformed ads x s backgrounds while this is a new area of research the current understanding is that abelian classical r matrices give rise to solutions of type iib supergravity while non abelian classical r matrices lead to solutions of the generalized supergravity equations we examine here some examples of non abelian classical r matrices and derive the associated backgrounds explicitly all of the resulting backgrounds satisfy the generalized equations for some of them we derive t dualized backgrounds by adding a linear coordinate dependence to the dilaton and show that these satisfy the usual type iib supergravity equations remarkably some of the t dualized backgrounds are locally identical to undeformed ads x s after an appropriate coordinate transformation but this seems not to be generally the case

stokes matrices poisson lie groups and frobenius manifolds the purpose of this paper is to point out and then draw some consequences of the fact that the poisson lie group g dual to g gln c may be identified with a certain moduli space of meromorphic connections over the unit disc having an irregular singularity at the origin g will be fully described in sect 2 the key feature of this point of view is that there is a holomorphic map g g from the dual of the lie algebra to the group g for each choice of diagonal matrix a0 with distinct eigenvalues the irregular type this map is essentially the riemann hilbert map or de rham morphism for such connections we will call it the monodromy map it is generically a local analytic isomorphism the main result is

quantum conjugacy classes of simple matrix groups let g be a simple complex classical group and mathfrak g its lie algebra let mathcal u hbar mathfrak g be the drinfeld jimbo quantization of the universal enveloping algebra mathcal u mathfrak g we construct an explicit mathcal u hbar mathfrak g equivariant quantization of conjugacy classes of g with levi subgroups as the stabilizers

the quantum group structure associated with non linearly extended virasoro algebras recently an infinite family of chiral virasoro vertex operators whose exchange algebra is given by the universalr matrix ofsl 2 q has been constructed in the present paper the case of non linearly w extended virasoro symmetries related to the algebrasan n 1 is considered along the same line contrary to the previous case a1 the standardr matrix ofsl n 1 q does not come out and a different solution of yang and baxter s equations is derived the associated quantum group structure is displayed

poisson lie interpretation of trigonometric ruijsenaars duality a geometric interpretation of the duality between two real forms of the complex trigonometric ruijsenaars schneider system is presented the phase spaces of the systems in duality are viewed as two different models of the same reduced phase space arising from a suitable symplectic reduction of the standard heisenberg double of u n the collections of commuting hamiltonians of the systems in duality are shown to descend from two families of free hamiltonians on the double which are dual to each other in a poisson lie sense our results give rise to a major simplification of ruijsenaars proof of the crucial symplectomorphism property of the duality map

on the exchange matrix for wznw model the connection between the exchange algebra in thesu 2 wess zumino novikov witten model and the quantum groupsu 2 is discussed it is shown that on the quasiclassical level this connection has the simple interpretation in terms of the lie poisson action ofsu 2 on the chiral components of the fields in the wznw model

quantum dressing orbits on compact groups the quantum double is shown to imply the dressing transformation on quantum compact groups and the quantum iwasawa decompositon in the general case quantum dressing orbits are described explicitly as algebras the dual coalgebras consisting of differential operators are related to the quantum weyl elements besides the differential geometry on a quantum leaf allows a remarkably simple construction of irreducible representations of the algebras of quantum functions representation spaces then consist of analytic functions on classical phase spaces these representations are also interpreted in the framework of quantization in the spirit of berezin applied to symplectic leaves on classical compact groups convenient coherent states are introduced and a correspondence between classical and quantum observables is given

superintegrability of geodesic motion on the sausage model reduction of the eta deformed sigma model on ads 5 x s 5 to the two dimensional squashed sphere s 2 eta can be viewed as a special case of the fateev sausage model where the coupling constant v i

courant algebroids poisson lie t duality and type ii supergravities we reexamine the notions of generalized ricci tensor and scalar curvature on a general courant algebroid reformulate them using objects natural w r t pull backs and reductions and obtain them from the variation of a natural action functional this allows us to prove in a very general setup the compatibility of the poisson lie t duality with the renormalization group flow and with string background equations we thus extend the known results to a much wider class of dualities including the cases with gauging so called dressing cosets or equivariant poisson lie t duality as an illustration we use the formalism to provide new classes of solutions of modified supergravity equations on symmetric spaces

a new model in the calogero ruijsenaars family hamiltonian reduction is used to project a trivially integrable system on the heisenberg double of su n n to obtain a system of ruijsenaars type on a suitable quotient space this system possesses bcn symmetry and is shown to be equivalent to the standard three parameter bcn hyperbolic sutherland model in the cotangent bundle limit

quasi hamiltonian geometry of meromorphic connections for each connected complex reductive group g we find a family of new examples of complex quasi hamiltonian g spaces with g valued moment maps these spaces arise naturally as moduli spaces of suitably framed meromorphic connections on principal g bundles over a disk and they generalise the conjugacy class example of alekseev malkin and meinrenken 3 which appears in the simple pole case using the fusion product in the theory this gives a finite dimensional construction of the natural symplectic structures on the spaces of monodromy stokes data of meromorphic connections over arbitrary genus riemann surfaces together with a new proof of the symplectic nature of isomonodromic deformations of such connections

minimal surfaces in q deformed rm ad rm s _ 5 s 5 with poincare coordinates we study minimal surfaces in q deformed s5 with a new coordinate system introduced in the previous work kameyama and yoshida 2015 j phys a math theor 48 075401 in this paper we introduce poincare coordinates for the deformed theory we then construct minimal surfaces whose boundary shape is a circle the solution corresponds to a 1 2 bps circular wilson loop in the limit a remarkable point is that the classical euclidean action is not divergent unlike the original this finiteness indicates that the q deformation may be regarded as a uv regularization

structures in bcn ruijsenaars schneider models we construct the classical r matrix structure for the lax formulation of bcn ruijsenaars schneider systems proposed in commun math phys 115 127 1988 the r matrix structure takes a quadratic form similar to the an ruijsenaars schneider poisson bracket behavior although the dynamical dependence is more complicated commuting hamiltonians stemming from the bcn ruijsenaars schneider lax matrix are shown to be linear combinations of particular koornwinder van diejen external fields ruijsenaars schneider models for specific values of the exponential one body couplings uniqueness of such commuting hamiltonians is established once the first of them and the general analytic structure are given

deformed integrable σ models classical r matrices and classical exchange algebra on drinfel d doubles we describe a unifying framework for the systematic construction of integrable deformations of integrable models within the hamiltonian formalism it applies equally to both the yang baxter type as well as gauged wzw type deformations which were considered recently in the literature as a byproduct these two families of integrable deformations are shown to be poisson lie t dual of one another

on q deformed symmetries as poisson lie symmetries and application to yang baxter type models this is an author created un copyedited version of an article accepted for publication in journal of physics a mathematical and theoretical the publisher is not responsible for any errors or omissions in this version of the manuscript or any version derived from it the version of record is available online at https doi org 1 1088 1751 8113 49 41 415402 2016 iop publishing ltd

spatially periodic orbits in coupled map lattices we obtain the conditions that ensure the stability of spatially and temporally periodic orbits of coupled map lattices the stability matrices can be put in a circulant and block circulant form this allows us to reduce the problem to smaller matrices corresponding to the building blocks of spatial periodicity we find that additional conditions are imposed as we expand the size of the lattice for the traveling wave solution the analysis is considerably simplified we have analyzed both the one dimensional and higher dimensional lattices

integrability of the eta deformed neumann rosochatius model an integrable deformation of the well known neumann rosochatius system is studied by considering generalised bosonic spinning solutions on the eta deformed ads 5 x s 5 background for this integra

non coboundary poisson lie structures on the book group all possible poisson lie pl structures on the 3d real lie group generated by a dilation and two commuting translations are obtained their classification is fully performed by relating these pl groups to the corresponding lie bialgebra structures on the corresponding book lie algebra by construction all these poisson structures are quadratic poisson hopf algebras for which the group multiplication is a poisson map in contrast to the case of simple lie groups it turns out that most of the pl structures on the book group are non coboundary ones moreover from the viewpoint of poisson dynamics the most interesting pl book structures are just some of these non coboundaries which are explicitly analysed in particular we show that the two different q deformed poisson versions of the sl 2 r algebra appear as two distinguished cases in this classification as well as the quadratic poisson structure that underlies the integrability of a large class of 3d lotka volterra equations finally the quantization problem for these pl groups is sketched

kitaev lattice models as a hopf algebra gauge theory we prove that kitaev s lattice model for a finite dimensional semisimple hopf algebra h is equivalent to the combinatorial quantisation of chern simons theory for the drinfeld double d h this shows that kitaev models are a special case of the older and more general combinatorial models this equivalence is an analogue of the relation between turaev viro and reshetikhin turaev tqfts and relates them to the quantisation of moduli spaces of flat connections we show that the topological invariants of the two models the algebra of operators acting on the protected space of the kitaev model and the quantum moduli algebra from the combinatorial quantisation formalism are isomorphic this is established in a gauge theoretical picture in which both models appear as hopf algebra valued lattice gauge theories we first prove that the triangle operators of a kitaev model form a module algebra over a hopf algebra of gauge transformations and that this module algebra is isomorphic to the lattice algebra in the combinatorial formalism both algebras can be viewed as the algebra of functions on gauge fields in a hopf algebra gauge theory the isomorphism between them induces an algebra isomorphism between their subalgebras of invariants which are interpreted as gauge invariant functions or observables it also relates the curvatures in the two models which are given as holonomies around the faces of the lattice this yields an isomorphism between the subalgebras obtained by projecting out curvatures which can be viewed as the algebras of functions on flat gauge fields and are the topological invariants of the two models

classical origin of quantum group symmetries in wess zumino witten conformal field theory we elucidate the way by which the quantum group symmetries of the wzw models arise within the canonical formalism of the classical field theory