deformed algebras from elliptic sl n algebras we extend to the case the results that we previously obtained on the construction of algebras from the elliptic algebra the elliptic algebra at the critical level c n has an extended center containing trace like operators t z families of poisson structures indexed by n n 1 2 integers defining q deformations of the algebra are constructed the operators t z also close an exchange algebra when for it becomes abelian when in addition p qnh where h is a non zero integer the poisson structures obtained in these classical limits contain different q deformed algebras depending on the parity of h characterizing the exchange structures at p qnh as new algebras

anticommutation in the presentations of theta deformed spheres abstract we consider an analogue of the deformed even spheres modifying the relations demanded of the self adjoint generator x in the usual presentation in this analogue x is given anticommutation relations with all of the other generators as opposed to being central the main result shows that these algebras satisfy a borsuk ulam property that is visible in even k theory

estimating and testing structural changes in multivariate regressions this paper considers issues related to estimation inference and computation with multiple structural changes that occur at unknown dates in a system of equations changes can occur in the regression coefficients and or the covariance matrix of the errors we also allow arbitrary restrictions on these parameters which permits the analysis of partial structural change models common breaks that occur in all equations breaks that occur in a subset of equations and so forth the method of estimation is quasi maximum likelihood based on normal errors the limiting distributions are obtained under more general assumptions than previous studies for testing we propose likelihood ratio type statistics to test the null hypothesis of no structural change and to select the number of changes structural change tests with restrictions on the parameters can be constructed to achieve higher power when prior information is present for computation an algorithm for an efficient procedure is proposed to construct the estimates and test statistics we also introduce a novel locally ordered breaks model which allows the breaks in different equations to be related yet not occurring at the same dates

estimation and inference in unstable nonlinear least squares models there is compelling evidence that many macroeconomic and financial variables are not generated by linear models this evidence is based on testing linearity against either smooth nonlinearity or piece wise linearity but there is no framework that encompasses both this paper provides an econometric framework that allows for both breaks and smooth nonlinearity in between breaks we estimate the unknown break dates simultaneously with other parameters via nonlinear least squares using new central limit results for nonlinear processes we provide inference methods on break dates and parameter estimates and several instability tests we illustrate our methods via simulated and empirical smooth transition models with breaks

tests for parameter instability and structural change with unknown change point this paper considers tests for parameter instability and structural change with unknown change point the results apply to a wide class of parametric models that are suitable for estimation by generalized method of moments procedures the asymptotic distributions of the test statistics considered here are nonstandard because the change point parameter only appears under the alternative hypothesis and not under the null the tests considered here are shown to have nontrivial asymptotic local power against all alternatives for which the parameters are nonconstant the tests are found to perform quite well in a monte carlo experiment reported elsewhere copyright 1993 by the econometric society

compact matrix pseudogroups the compact matrix pseudogroup is a non commutative compact space endowed with a group structure the precise definition is given and a number of examples is presented among them we have compact group of matrices duals of discrete groups and twisted deformed su n groups the representation theory is developed it turns out that the tensor product of representations depends essentially on their order the existence and the uniqueness of the haar measure is proved and the orthonormality relations for matrix elements of irreducible representations are derived the form of these relations differs from that in the group case this is due to the fact that the haar measure on pseudogroups is not central in general the corresponding modular properties are discussed the haar measures on the twistedsu 2 group and on the finite matrix pseudogroup are found

structural break models under mis specification implications for forecasting abstract this paper revisits the least squares estimator of the linear regression with a structural break we view the model as an approximation to the true data generating process whose exact nature is unknown but perhaps changing over time either continuously or with some jumps this view is widely held in the forecasting literature and under this view the time series dependence property of all the observed variables is unstable as well we establish that the rate of convergence of the estimator to a properly defined limit is at most the cube root of t where t is the sample size which is much slower than the standard super consistent rate we also provide an asymptotic distribution of the estimator and that of the gaussian quasi likelihood ratio statistic for a certain class of true data generating processes we relate our finding to current forecast combination methods and propose a new averaging scheme our method compares favourably with various contemporary forecasting methods in forecasting a number of macroeconomic series

quantum 401 1401 1401 1algebras and macdonald polynomials we derive a quantum deformation of thew n algebra and its quantum miura transformation whose singular vectors realize the macdonald polynomials

equivariant poincare duality for quantum group actions we extend the notion of poincare duality in kk theory to the setting of quantum group actions an important ingredient in our approach is the replacement of ordinary tensor products by braided tensor products along the way we discuss general properties of equivariant kk theory for locally compact quantum groups including the construction of exterior products as an example we prove that the standard podle sphere is equivariantly poincare dual to itself

a new approach to induction and imprimitivity results given a closed quantum subgroup of a locally compact quantum group we study induction of unitary corepresentations of the quantum subgroup to the ambient quantum group more generally we study induction given a coaction of the quantum subgroup on a c algebra we prove imprimitivity theorems that unify the existing theorems for actions and coactions of groups this means that we deflne quantum homogeneous spaces as c algebras and that we prove morita equivalence of crossed products and homogeneous spaces we essentially use von neumann algebraic techniques to prove these morita equivalences between c algebras the theory of induced representations of locally compact l c groups was introduced by mackey 21 who discovered the imprimitivity theorem characterizing induced representations through the presence of a covariant representation of a homogeneous space riefiel 26 provided a modern approach using the language of hilbert c modules after the work of riefiel several induction procedures and imprimitivity results have been obtained both for actions and for coactions of groups we shall brie y review them below the purpose of this paper is to develop such an induction and imprimitivity machinery in the setting of locally compact quantum groups 16 17 in this way we provide a unifled approach to several results on actions and coactions of groups on c algebras at the same time our proofs in the setting of l c quantum groups are simpler than the classical proofs dealing with coactions of groups another motivation comes from quantum group theory meyer and nest have undertaken a reformulation of the baum connes conjecture 24 in which induction and restriction play a crucial role the development of induction and imprimitivity in the current paper should play an equally important role in the formulation of a baum connes conjecture for quantum groups

finite dimensional irreducible representations of twisted yangians we study quantized enveloping algebras called twisted yangians they are analogs of the yangian y gl n for the classical lie algebras of b c and d series the twisted yangians are subalgebras in y gl n and coideals with respect to the coproduct in y gl n we give a complete description of their finite dimensional irreducible representations every such representation is highest weight and we give necessary and sufficient conditions for an irreducible highest weight representation to be finite dimensional the result is analogous to drinfeld s theorem for the ordinary yangians its detailed proof for the a series is also reproduced for the simplest twisted yangians we construct an explicit realization for each finite dimensional irreducible representation in tensor products of representations of the corresponding lie algebras

estimating and testing linear models with multiple structural changes this paper develops the statistical theory for testing and estimating multiple change points in regression models the rate of convergence and limiting distribution for the estimated parameters are obtained several test statistics are proposed to determine the existence as well as the number of change points a partial structural change model is considered the authors study both fixed and shrinking magnitudes of shifts in addition the models allow for serially correlated disturbances mixingales an estimation strategy for which the location of the breaks need not be simultaneously determined is discussed instead the authors method successively estimates each break point

yangian realisations from finite w algebras we construct an algebra homomorphism between the yangian y sl n and the finite algebras sl np n sl p for any p we show how this result can be applied to determine properties of the finite dimensional representations of such algebras

testing for common breaks in a multiple equations system abstract the issue addressed in this paper is that of testing for common breaks across or within equations of a multivariate system our framework is very general and allows integrated regressors and trends as well as stationary regressors the null hypothesis is that breaks in different parameters occur at common locations and are separated by some positive fraction of the sample size unless they occur across different equations under the alternative hypothesis the break dates across parameters are not the same and also need not be separated by a positive fraction of the sample size whether within or across equations the test considered is the quasi likelihood ratio test assuming normal errors though as usual the limit distribution of the test remains valid with non normal errors of independent interest we provide results about the rate of convergence of the estimates when searching over all possible partitions subject only to the requirement that each regime contains at least as many observations as some positive fraction of the sample size allowing break dates not separated by a positive fraction of the sample size across equations simulations show that the test has good finite sample properties we also provide an application to issues related to level shifts and persistence for various measures of inflation to illustrate its usefulness

quantized algebras of functions on homogeneous spaces with poisson stabilizers let g be a simply connected semisimple compact lie group with standard poisson structure k a closed poisson lie subgroup 0 q 1 we study a quantization c gq kq of the algebra of continuous functions on g k using results of soibelman and dijkhuizen stokman we classify the irreducible representations of c gq kq and obtain a composition series for c gq kq we describe closures of the symplectic leaves of g k refining the well known description in the case of flag manifolds in terms of the bruhat order we then show that the same rules describe the topology on the spectrum of c gq kq next we show that the family of c algebras c gq kq 0 q 1 has a canonical structure of a continuous field of c algebras and provides a strict deformation quantization of the poisson algebra mathbb c g k finally extending a result of nagy we show that c gq kq is canonically kk equivalent to c g k

quantum spheres and projective spaces as graph algebras the c algebras of continuous functions on quantum spheres quantum real projective spaces and quantum complex projective spaces are realized as cuntz krieger algebras corresponding to suitable directed graphs structural results about these quantum spaces especially about their ideals and k theory are then derived from the general theory of graph algebras it is shown that the quantum even and odd dimensional spheres are produced by repeated application of a quantum double suspension to two points and the circle respectively

the baum connes conjecture for free orthogonal quantum groups we prove an analogue of the baum connes conjecture for free orthogonal quantum groups more precisely we show that these quantum groups have a element and that 1 it follows that free orthogonal quantum groups are k amenable we compute explicitly their k theory and deduce in the unimodular case that the corresponding reduced c algebras do not contain nontrivial idempotents our approach is based on the reformulation of the baum connes conjecture by meyer and nest using the language of triangulated categories an important ingredient is the theory of monoidal equivalence of compact quantum groups developed by bichon de rijdt and vaes this allows us to study the problem in terms of the quantum group suq 2 the crucial part of the argument is a detailed analysis of the equivariant kasparov theory of the standard podle

invariants in noncommutative dynamics abstract when a compact quantum group h coacts freely on unital c algebras a and b the existence of equivariant maps a b may often be ruled out due to the incompatibility of some invariant we examine the limitations of using invariants both concretely and abstractly to resolve the noncommutative borsuk ulam conjectures of baum d browski hajac among our results we find that for certain finite dimensional h there can be no well behaved invariant which solves the type 1 conjecture for all free coactions of h this claim is in stark contrast to the case when h is finite dimensional and abelian in the same vein it is possible for all iterated joins of h to be cleft as comodules over the hopf algebra associated to h finally two commonly used invariants the local triviality dimension and the spectral count may both change in a deformation procedure

inference regarding multiple structural changes in linear models with endogenous regressors this paper considers the linear model with endogenous regressors and multiple changes in the parameters at unknown times it is shown that minimization of a generalized method of moments criterion yields inconsistent estimators of the break fractions but minimization of the two stage least squares 2sls criterion yields consistent estimators of these parameters we develop a methodology for estimation and inference of the parameters of the model based on 2sls the analysis covers the cases where the reduced form is either stable or unstable the methodology is illustrated via an application to the new keynesian phillips curve for the us

estimating restricted structural change models abstract this paper considers issues related to multiple structural changes occurring at unknown dates in the linear regression model when restrictions are imposed on the parameters this includes for example the important special case where different nonadjacent regimes are the same the estimates are constructed as global minimizers of the restricted sum of squared residuals and we provide an extension of the algorithm discussed in bai and perron 2003b computation and analysis of multiple structural change models journal of applied econometrics 18 1 22 to efficiently compute them we show that the estimates of the break dates have the same asymptotic properties with or without the restrictions imposed that is in large samples there is no efficiency gain from imposing valid restrictions as far as the estimates of the break dates are concerned of course efficiency gains occur for the other parameters of the model simulations show that in small samples all parameters are more efficiently estimated using the restrictions we also consider tests of the null hypothesis of no structural change these are also more powerful when the restrictions are imposed a gauss code for all the procedures discussed in this paper is available from the authors

principal realization of the yangian y gl n motivated to simplify the structure of tensor representations we give a new set of generators for the yangian y sl n using the principal realization in simple lie algebras the isomorphism between our new basis and the standard cartan weyl basis is also given we show by example that the principal basis simplifies the yangian action significantly in the tensor product of the fundamental representation and its dual

the limit distribution of the estimates in cointegrated regression models with multiple structural changes abstract we study estimation and inference in cointegrated regression models with multiple structural changes allowing both stationary and integrated regressors both pure and partial structural change models are analyzed we derive the consistency rate of convergence and the limit distribution of the estimated break fractions our technical conditions are considerably less restrictive than those in bai et al bai j lumsdaine r l stock j h 1998 testing for and dating breaks in multivariate time series review of economic studies 65 395 432 who considered the single break case in a multi equations system and permit a wide class of practically relevant models our analysis is however restricted to a single equation framework we show that if the coefficients of the integrated regressors are allowed to change the estimated break fractions are asymptotically dependent so that confidence intervals need to be constructed jointly if however only the intercept and or the coefficients of the stationary regressors are allowed to change the estimates of the break dates are asymptotically independent as in the stationary case analyzed by bai and perron bai j perron p 1998 estimating and testing linear models with multiple structural changes econometrica 66 47 78 we also show that our results remain valid under very weak conditions when the potential endogeneity of the non stationary regressors is accounted for via an increasing sequence of leads and lags of their first differences as additional regressors simulation evidence is presented to assess the adequacy of the asymptotic approximations in finite samples

rtt presentation of finite algebras we construct a wide class of finite algebras as truncations of yangians these truncations correspond to algebra homomorphisms and allow us to construct the algebras as exchange algebras the r matrix being the yangian one as an application we classify all irreducible finite dimensional representations of these algebras and determine their centre

equivariant comparison of quantum homogeneous spaces we consider the quantum homogeneous spaces of the q deformation of simply connected simple compact lie groups and their poisson lie quantum subgroups we prove the deformation invariance in the equivariant kk theory with respect to the translation action by maximal tori this extends a result of neshveyev and tuset to the equivariant setting as applications we prove the ring isomorphism of the k homology of gq with respect to the coproduct of c gq and an analogue of the borsuk ulam theorem for quantum spheres

yangian symmetry in the nonlinear schrodinger hierarchy we study the yangian symmetry of the multicomponent quantum nonlinear schrodinger hierarchy in the framework of the quantum inverse scattering method we give an explicit realization of the yangian generators in terms of the deformed oscillators algebra which naturally occurs in this framework