reduced notation inner plethysms and the symmetric group the reduced notation for irreducible representations of the symmetric group s is interpreted in terms of symmetric formal series and vertex operators and is used to prove a number of properties of reduced kronecker products and inner plethysms in an n independent manner conditions for self associativity of kronecker products and inner plethysms are established reduced inner plethysms are developed and applied to the question of non simple phase groups among the symmetric sn and alternating an groups

a test for second order stationarity and approximate confidence intervals for localized autocovariances for locally stationary time series summary many time series are not second order stationary and it is not appropriate to analyse them by using methods designed for stationary series the paper introduces a new test for second order stationarity that detects kinds of departures from stationarity that are different from those based on fourier methods the new test is also computationally fast designed to work with gaussian and a wide range of non gaussian time series and can locate non stationarities in time and scale the test is demonstrated on earthquake explosion infant electrocardiogram and simulated time series showing varying degrees of stationarity the second main contribution develops approximate confidence intervals for time varying autocovariances for locally stationary series as the usual bands computed for stationary series are not appropriate our new bands enable practitioners to assess time varying autocovariances statistically and are exhibited on localized autocovariances of explosion and simulated time series

irreducible calibrated representations of periplectic brauer algebras and hook representations of the symmetric group abstract we construct an infinite tower of irreducible calibrated representations of periplectic brauer algebras on which the cup cap generators act by nonzero matrices as representations of the symmetric group these are exterior powers of the standard representation i e hook representations our approach uses the recently defined degenerate affine periplectic brauer algebra which plays a role similar to that of the degenerate affine hecke algebra in representation theory of the symmetric group we write formulas for the representing matrices in the basis of jucys murphy eigenvectors and we completely describe the spectrum of these representations the tower formed by these representations provides a new non semisimple categorification of pascal s triangle along the way we also prove some basic results about calibrated representations of the degenerate affine periplectic brauer algebra

a differential operator for symmetric functions and the combinatorics of multiplying transpositions by means of irreducible characters for the symmetric group formulas have previously been given for the number of ways of writing permutations in a given conjugacy class as products of transpositions these formulas are alternating sums of binomial coefficients and powers of integers combinatorial proofs are obtained in this paper by analyzing the action of a partial differential operator for symmetric functions

ideal spatial adaptation by wavelet shrinkage summary with ideal spatial adaptation an oracle furnishes information about how best to adapt a spatially variable estimator whether piecewise constant piecewise polynomial variable knot spline or variable bandwidth kernel to the unknown function estimation with the aid of an oracle offers dramatic advantages over traditional linear estimation by nonadaptive kernels however it is a priori unclear whether such performance can be obtained by a procedure relying on the data alone we describe a new principle for spatially adaptive estimation selective wavelet reconstruction we show that variable knot spline fits and piecewise polynomial fits when equipped with an oracle to select the knots are not dramatically more powerful than selective wavelet reconstruction with an oracle we develop a practical spatially adaptive method riskshrink which works by shrinkage of empirical wavelet coefficients riskshrink mimics the performance of an oracle for selective wavelet reconstruction as well as it is possible to do so a new inequality in multivariate normal decision theory which we call the oracle inequality shows that attained performance differs from ideal performance by at most a factor of approximately 2 log n where n is the sample size moreover no estimator can give a better guarantee than this within the class of spatially adaptive procedures riskshrink is essentially optimal relying only on the data it comes within a factor log 2 n of the performance of piecewise polynomial and variableknot spline methods equipped with an oracle in contrast it is unknown how or if piecewise polynomial methods could be made to function this well when denied access to an oracle and forced to rely on data alone

consistent classification of nonstationary time series using stochastic wavelet representations consider the situation when we have training data containing many time series having known group membership and testing data with unknown group membership the goals are to find timescale features using training data that can best separate the groups and to use these highly discriminant features to classify test data we propose a method for classification using a bias corrected nondecimated wavelet transform wavelets are ideal for identifying highly discriminant local time and scale features the observed signals will be treated as realizations of locally stationary wavelet processes under which we define and rigorously estimate the evolutionary wavelet spectrum timescale decomposition of variance the evolutionary wavelet spectrum which contains the second moment information on the signals is used as the classification signature for each test time series we compute the empirical wavelet spectrum and its divergence from the wavelet spectrum of each group the test time series is then assigned

forecasting multifractal volatility this paper develops analytical methods to forecast the distribution of future returns for a new continuous time process the poisson multifractal the process captures the thick tails volatility persistence and moment scaling exhibited by many financial time series it can be interpreted as a stochastic volatility model with multiple frequencies and a markov latent state we assume for simplicity that the forecaster knows the true generating process with certainty but only observes past returns the challenge in this environment is long memory and the corresponding infinite dimension of the state space we introduce a discretized version of the model that has a finite state space and an analytical solution to the conditioning problem as the grid step size goes to zero the discretized model weakly converges to the continuous time process implying the consistency of the density forecasts

vertex algebras and the class algebras of wreath products the jucys murphy elements for wreath products gamma n gamma wr s n associated to any finite group gamma are introduced and they play an important role in our study of the connections between class algebras of gamma n for all n and vertex algebras we construct an action of a variant of the mathcal w 1 infty algebra acting irreducibly on the direct sum mathcal r gamma of the class algebras of gamma n for all n in a group theoretic manner we establish various relations between convolution operators using jm elements and heisenberg algebra operators acting on mathcal r gamma as applications we obtain two distinct sets of algebra generators for the class algebra of gamma n and establish various stability results concerning products of normalized conjugacy classes of gamma n and the power sums of jucys murphy elements etc we introduce a stable algebra which encodes the class algebra structures of gamma n for all n whose structure constants are shown to be non negative integers in the symmetric group case that is when gamma is trivial we recover and strengthen in a uniform approach various results of lascoux and thibon kerov and olshanski and farahat and higman etc

spectrum estimation by wavelet thresholding of multitaper estimators current methods for power spectrum estimation by wavelet thresholding use the empirical wavelet coefficients derived from the log periodogram unfortunately the periodogram is a very poor estimate when the true spectrum has a high dynamic range and or is rapidly varying in addition because the distribution of the log periodogram is markedly non gaussian special wavelet dependent thresholding schemes are needed these difficulties can be bypassed by starting with a multitaper spectrum estimator the logarithm of this estimator is close to gaussian distributed if a moderate number spl ges 5 of tapers are used in contrast to the log periodogram log multitaper estimates are not approximately pairwise uncorrelated at the fourier frequencies but the form of the correlation can be accurately and simply approximated for scale independent thresholding the correlation acts in accordance with the wavelet shrinkage paradigm to suppress small scale noise spikes while leaving informative coarse scale coefficients relatively unattenuated this simple approach to spectrum estimation is demonstrated to work very well in practice additionally the progression of the variance of wavelet coefficients with scale can be accurately calculated allowing the use of scale dependent thresholds this more involved approach also works well in practice but is not uniformly preferable to the scale independent approach

nonparametric quasi maximum likelihood estimation for gaussian locally stationary processes this paper deals with nonparametric maximum likelihood estimation for gaussian locally stationary processes our nonparametric mle is constructed by minimizing a frequency domain likelihood over a class of functions the asymptotic behavior of the resulting estimator is studied the results depend on the richness of the class of functions both sieve estimation and global estimation are considered our results apply in particular to estimation under shape constraints as an example autoregressive model fitting with a monotonic variance function is discussed in detail including algorithmic considerations a key technical tool is the time varying empirical spectral process indexed by functions for this process a bernstein type exponential inequality and a central limit theorem are derived these results for empirical spectral processes are of independent interest

vertex operators symmetric functions and the spin group γn abstract this work provides a vertex operator approach to the symmetric group sn and its double covering group n by generalizing a result of frenkel and sato for sn we formulate a correspondence between the space v of certain twisted vertex operators the ring of symmetric functions over q 2 and the space of nontrivial irreducible characters of n under this identification we show that a distinguished orthogonal basis of v corresponds to the set of nontrivial irreducible characters of n where both are parametrized by partitions with odd integer parts the counterpart of this distinguished basis in the ring over q 2 is the set of schur s q functions which are loosely speaking the square roots of the schur functions the nontrivial part of the character table of n is shown to be given by certain matrix coefficients in v

vertex operators and symmetric functions an algorithm for the calculation of q dependent spin characters of the symmetric group is given with an explicit example of s4 a method for constructing the q analogue of the vertex operators is developed a 1 1 correspondence between the space v of twisted q vertex operators and the ring of q deformed symmetric functions lambda x zq q t is established and a mapping from v to lambda x zq q t is defined a number of relevant theorems are given

representation theory of the yokonuma hecke algebra abstract we develop an inductive approach to the representation theory of the yokonuma hecke algebra y d n q based on the study of the spectrum of its jucys murphy elements which are defined here we give explicit formulas for the irreducible representations of y d n q in terms of standard d tableaux we then use them to obtain a semisimplicity criterion finally we prove the existence of a canonical symmetrising form on y d n q and calculate the schur elements with respect to that form

vertex operators arising from jacobi trudi identities we give an interpretation of the boson fermion correspondence as a direct consequence of the jacobi trudi identity this viewpoint enables us to construct from a generalized version of the jacobi trudi identity the action of a clifford algebra on the polynomial algebras that arrive as analogues of the algebra of symmetric functions a generalized giambelli identity is also proved to follow from that identity as applications we obtain explicit formulas for vertex operators corresponding to characters of the classical lie algebras shifted schur functions and generalized schur symmetric functions associated to linear recurrence relations

symmetric groups and the cup product on the cohomology of hilbert schemes let c sn be the z module of integer valued class functions on the symmetric group sn we introduce a graded version of the con volution product on c sn and show that there is a degree preserving ring isomorphism c sn h hilb n a 2 z to the cohomology of the hilbert scheme of points in the complex affine plane

symmetric function products and plethysms and the boson fermion correspondence we use the boson fermion correspondence for s and q functions to establish some interesting properties concerning outer products and plethysms of s functions or q functions by power sum symmetric functions the techniques which are developed are also applied to computing the inverse kostka foulkes matrix which is the transition matrix between hall littlewood symmetric functions and s functions in some simple cases

wavelet processes and adaptive estimation of the evolutionary wavelet spectrum this article defines and studies a new class of non stationary random processes constructed from discrete non decimated wavelets which generalizes the cramer fourier representation of stationary time series we define an evolutionary wavelet spectrum ews which quantifies how process power varies locally over time and scale we show how the ews may be rigorously estimated by a smoothed wavelet periodogram and how both these quantities may be inverted to provide an estimable time localized autocovariance we illustrate our theory with a pedagogical example based on discrete non decimated haar wavelets and also a real medical time series example

heisenberg algebra and hilbert schemes of points on projective surfaces the purpose of this paper is to throw a bridge between two seemingly unrelated subjects one is the hilbert scheme of points on projective surfaces which has been intensively studied by various people see e g i br es g61 g62 the other is the infinite dimensional heisenberg algebra which is closely related to affine lie algebras see e g k we shall construct a representation of the heisenberg algebra on the homology group of the hilbert scheme in other words the homology group will become a fock space the basic idea is to introduce certain correspondences in the product of the hilbert scheme then they define operators on the homology group by a well known procedure they give generators of the heisenberg algebra and the only thing we must check is that they satisfy the defining relation here we remark that the components of the hilbert scheme are parameterized by numbers of points and our representation will be constructed on the direct sum of homology groups of all components our correspondences live in the product of the different components thus it is quite essential to study all components together our construction has the same spirit as the author s construction nal na4 of representations of affine lie algebras on homology groups of moduli spaces of instantons 1 on ale spaces which are minimal resolutions of simple singularities certain correspondences called hecke correspondences were used to define operators these twist instantons along curves irreducible components of the exceptional set while ours twist ideals around points in fact the hilbert scheme of points can be considered as the moduli space of rank 1 vector bundles or more precisely torsion free sheaves our construction should be considered as a first step to extend nal na4 to general 4 manifolds the same program was also proposed by ginzburg kapranov and vasserot gkv

the farahat higman ring of wreath products and hilbert schemes we study the structure constants of the class algebra rz n of the wreath products n associated to an arbitrary finite group with respect to the basis of conjugacy classes we show that a suitable filtration on rz n gives rise to the graded ring g n with non negative integer structure constants independent of n some of which are computed which are then encoded in a farahat higman ring g the real conjugacy classes of come to play a distinguished role and are treated in detail in the case when is a subgroup of sl2 c the above results provide new insight to the cohomology rings of hilbert schemes of points on a quasi projective surface x

wavelet thresholding techniques for power spectrum estimation estimation of the power spectrum s f of a stationary random process can be viewed as a nonparametric statistical estimation problem we introduce a nonparametric approach based on a wavelet representation for the logarithm of the unknown s f this approach offers the ability to capture statistically significant components of ln s f at different resolution levels and guarantees nonnegativity of the spectrum estimator the spectrum estimation problem is set up as a problem of inference on the wavelet coefficients of a signal corrupted by additive non gaussian noise we propose a wavelet thresholding technique to solve this problem under specified noise resolution tradeoffs and show that the wavelet coefficients of the additive noise may be treated as independent random variables the thresholds are computed using a saddle point approximation to the distribution of the noise coefficients

schur functions and affine lie algebras abstract we make use of the representation theory of the infinite dimensional lie algebrasa b and formula to derive explicit formulas relating schur sp functions to schur ss functions

plethysms replicated schur functions and series with applications to vertex operators specializations of schur functions are exploited to define and evaluate the schur functions s x and plethysms s s x for any integer real or complex plethysms are then used to define pairs of mutually inverse infinite series of schur functions m and l specified by arbitrary partitions these are used in turn to define and provide generating functions for formal characters s of certain groups h thereby extending known results for orthogonal and symplectic group characters each of these formal characters is then given a vertex operator realization first in terms of the seriesm m 0 and various l dual to l and then more explicitly in the exponential form finally the replicated form of such vertex operators are written down the characters of the orthogonal and symplectic groups have been found by schur 34 and weyl 35 respectively the method used is transcendental and depends on integration over the group manifold these characters however may be obtained by purely algebraic methods this algebraic method would seem to offer a better prospect of successful application to other restricted groups than the method of group integration littlewood d e 1944 phil trans r soc london ser a 239 809 392 pacs numbers 02 10 v 02 10 de 02 20 a 02 20 hj mathematics subject classification 05e05 17b69 11e57 16w30 20e22 33d52 43a40 1751 8113

the deformed virasoro algebra at roots of unity we discuss some aspects of the representation theory of the deformed virasoro algebra virpq in particular we give a proof of the formula for the kac determinant and then determine the center of virp q for q a primitive nth root of unity we derive explicit expressions for the generators of the center in the limit t qp 1 and elucidate the connection to the hall littlewood symmetric functions furthermore we argue that for the algebra describes gentile statistics of order n 1 i e a situation in which at most n 1 particles can occupy the same state

a test for the absence of aliasing or local white noise in locally stationary wavelet time series aliasing is often overlooked in time series analysis but can seriously distort the spectrum autocovariance and their estimates we show that dyadic subsampling of a locally stationary wavelet process which can cause aliasing results in a process that is the sum of asymptotic white noise and another locally stationary wavelet process with a modified spectrum we develop a test for the absence of aliasing in a locally stationary wavelet series at a fixed location and illustrate it on simulated data and a wind energy time series a useful by product is a new test for local white noise the tests are robust to model misspecification in that it is unnecessary for the analysis and synthesis wavelets to be identical hence in principle the tests work irrespective of which wavelet is used to analyze the time series though in practice there is a tradeoff between increasing statistical power and time localization of the test

vertex operators and composite supersymmetric s functions the s function basis for the fock space of vertex operator constructions is considered where states are associated with partitions mod lambda the authors show that the matrix element lambda mod valpha z mod mu is essentially given by the composite s function slambda mu z where the argument z identical to z 1 is replicated mod alpha mod times matrix elements of products of vertex operators lambda mod valpha z v beta w mod mu are given up to functions of z w independent of lambda and mu by the composite supersymmetric s function slambda mu z w where the z w are replicated mod alpha mod mod beta mod times the supersymmetric arguments being those associated with negative roots

two constructions of affine lie algebra representations and boson fermion correspondence in quantum field theory we establish an isomorphism between the vertex and spinor representations of affine lie algebras for types dl 1 and dl 1 2 we also study decomposition of spinor representations using the infinite family of casimir operators and prove that they are either irreducible or have two irreducible components we show that the vertex and spinor constructions of the representations can be reformulated in the language of two dimensional quantum field theory in this physical context the two constructions yield the generalized sine gordon and thirring models respectively already in renormalized form the isomorphism of representations implies an equivalence of these two models which is known in quantum field theory as the boson fermion correspondence

generators of the hecke algebra of s2n bn abstract in analogy with the set of jucys murphy elements a set of ring generators for the hecke algebra of the gel fand pair s 2 n b n where b n is the hyperoctahedral subgroup of the symmetric group s 2 n is constructed various consequences are presented a conjecture of s matsumoto is proven

estimating linear dependence between nonstationary time series using the locally stationary wavelet model large volumes of neuroscience data comprise multiple nonstationary electrophysiological or neuroimaging time series recorded from different brain regions accurately estimating the dependence between such neural time series is critical since changes in the dependence structure are presumed to reflect functional interactions between neuronal populations we propose a new dependence measure derived from a bivariate locally stationary wavelet time series model since wavelets are localized in both time and scale this approach leads to a natural local and multi scale estimate of nonstationary dependence our methodology is illustrated by application to a simulated example and to electrophysiological data relating to interactions between the rat hippocampus and prefrontal cortex during working memory and decision making

equivariant gw theory of stacky curves we extend okounkov and pandharipande s work on the equivariant gromov witten theory of mathbb p 1 to a class of stacky curves mathcal x our main result uses virtual localization and the orbifold elsv formula to express the tau function tau mathcal x as a vacuum expectation on a fock space

vertex operator realization of symplectic and orthogonal s functions it is shown that symplectic and orthogonal schur functions can be realized by the action of the modes of certain vertex operators on the function the properties of these vertex operators allow one to reproduce the basic propreties of these types of symmetric functions the vertex operator modes are shown to obey free fermionic relations which provide applications such as calculating products and plethysms as well as generating hirota type partial differential equations pdes which have symplectic s functions as functions

an explicit formula for the characters of the symmetric group we give an explicit expression of the normalized characters of the symmetric group in terms of the contents of the partition labelling the representation

multiple change point detection for high dimensional time series via sparsified binary segmentation time series segmentation a k a multiple change point detection is a well established problem however few solutions are designed specifically for high dimensional situations in this paper our interest is in segmenting the second order structure of a high dimensional time series in a generic step of a binary segmentation algorithm for multivariate time series one natural solution is to combine cusum statistics obtained from local periodograms and cross periodograms of the components of the input time series however the standard maximum and average methods for doing so often fail in high dimensions when for example the change points are sparse across the panel or the cusum statistics are spuriously large in this paper we propose the sparsified binary segmentation sbs algorithm which aggregates the cusum statistics by adding only those that pass a certain threshold this sparsifying step reduces the impact of irrelevant noisy contributions which is particularly beneficial in high dimensions in order to show the consistency of sbs we introduce the multivariate locally stationary wavelet model for time series which is a separate contribution of this work

structural break estimation for nonstationary time series models this article considers the problem of modeling a class of nonstationary time series using piecewise autoregressive ar processes the number and locations of the piecewise ar segments as well as the orders of the respective ar processes are assumed unknown the minimum description length principle is applied to compare various segmented ar fits to the data the goal is to find the best combination of the number of segments the lengths of the segments and the orders of the piecewise ar processes such a best combination is implicitly defined as the optimizer of an objective function and a genetic algorithm is implemented to solve this difficult optimization problem numerical results from simulation experiments and real data analyses show that the procedure has excellent empirical properties the segmentation of multivariate time series is also considered assuming that the true underlying model is a segmented autoregression this procedure is shown to be consistent for estimating the location of

vertex algebras and the cohomology ring structure of hilbert schemes of points on surfaces using vertex algebra techniques we determine a set of generators for the cohomology ring of the hilbert schemes of points on an arbitrary smooth projective surface over the field of complex numbers

estimation of ambiguity functions with limited spread in this correspondence we propose a class of estimators of the ambiguity function of a discrete time process using thresholding to this purpose the distributional and moment properties of the empirical ambiguity function for a realization of an analytic random process are derived and the moments for the special cases of stationary uniformly modulated and deterministic signals immersed in noise processes are determined suitable thresholds are chosen based on the distributional properties of the empirical ambiguity function and the procedure is tested on simulated data

multiscale variance stabilization via maximum likelihood this article proposes maximum likelihood approaches for multiscale variance stabilization mvs tranforms for independently and identically distributed data for two mvs transforms we present new unified theoretical results on their jacobians which are a key component of the likelihood the new results provide i a deeper theoretical understanding of the transforms and ii the ability to compute the likelihood in linear time compared to previous numerical methods which required quadratic effort the new mvs transforms are shown empirically to compare favourably to the well known box cox transform and almost dominate it we show how the new transforms like box cox can facilitate simpler models by an example involving the famous wool data

infinite dimensional diffusions as limits of random walks on partitions starting with finite markov chains on partitions of a natural number n we construct via a scaling limit transition as n a family of infinite dimensional diffusion processes the limit processes are ergodic their stationary distributions the so called z measures appeared earlier in the problem of harmonic analysis for the infinite symmetric group the generators of the processes are explicitly described

generalized symplectic schur functions and suc hierarchy in this paper we first define a generalization of the symplectic schur functions and their vertex operator realizations by means of the vertex operators we obtain a series of non linear partial differential equations of infinite order the symplectic uc hierarchy called the suc hierarchy we regard it as an extension of the symplectic kp hierarchy

the uncertainty of storm season changes quantifying the uncertainty of autocovariance changepoints in oceanography there is interest in determining storm season changes for logistical reasons such as equipment maintenance scheduling in particular there is interest in capturing the uncertainty associated with these changes in terms of the number and location of them such changes are associated with autocovariance changes this article proposes a framework to quantify the uncertainty of autocovariance changepoints in time series motivated by this oceanographic application more specifically the framework considers time series under the locally stationary wavelet lsw framework deriving a joint density for scale processes in the raw wavelet periodogram by embedding this density within a hidden markov model hmm framework we consider changepoint characteristics under this multiscale setting such a methodology allows us to model changepoints and their uncertainty for a wide range of models including piecewise second order stationary processes for example piecewise moving average processes

a new cohomology theory of orbifold based on the orbifold string theory model in physics we construct a new cohomology ring for any almost complex orbifold the key theorem is the associativity of this new ring some examples are computed

nonlocal robin laplacians and some remarks on a paper by filonov on eigenvalue inequalities abstract the aim of this paper is twofold first we characterize an essentially optimal class of boundary operators which give rise to self adjoint laplacians in l 2 d n x with nonlocal and local robin type boundary conditions on bounded lipschitz domains r n n n n 2 second we extend friedlander s inequalities between neumann and dirichlet laplacian eigenvalues to those between nonlocal robin and dirichlet laplacian eigenvalues associated with bounded lipschitz domains following an approach introduced by filonov for this type of problems

a haar fisz technique for locally stationary volatility estimation summary we consider a locally stationary model for financial log returns whereby the returns are independent and the volatility is a piecewise constant function with jumps of an unknown number and locations defined on a compact interval to enable a meaningful estimation theory we demonstrate that the model explains well the common characteristics of log returns we propose a new wavelet thresholding algorithm for volatility estimation in this model in which haar wavelets are combined with the variance stabilising fisz transform the resulting volatility estimator is mean square consistent with a near parametric rate does not require any pre estimates is rapidly computable and is easily implemented we also discuss important variations on the choice of estimation parameters we show that our approach both gives a very good fit to selected currency exchange datasets and achieves accurate long and short term volatility forecasts in comparison to the garch 1 1 and moving window techniques

wreath hecke algebras and centralizer construction for wreath products abstract generalizing the centralizer construction of molev and olshanski on symmetric groups we study the structures of the centralizer z m n of the wreath product g n m in the group algebra of g n for any n m we establish the connection between z m n and a generalization of degenerate affine hecke algebras introduced in our earlier work

virasoro algebra and wreath product convolution abstract we present a group theoretic construction of the virasoro algebra in the framework of wreath products this can be regarded as a counterpart of a geometric construction of lehn in the theory of hubert schemes of points on a surface

vertex operators and hall littlewood symmetric functions abstract we consider vertex operators on space v with a parameter t their components form an associative algebra which is a generalization of the clifford algebra a distinguished orthogonal basis of v is proved to be the hall littlewood symmetric functions we show that kostka foulkes polynomials or certain kazhdan lusztig polynomials for the affine weyl group of type a are matrix coefficients on the space v we also obtain certain generating functions for the product of hall littlewood functions and the kostka foulkes polynomials

the cup product of hilbert schemes for k3 surfaces to any graded frobenius algebra a we associate a sequence of graded frobenius algebras a n so that there is canonical isomorphism of rings h x 2 n h x n 2n for the hilbert scheme x n of generalised n tuples of any smooth projective surface x with numerically trivial canonical bundle

hopf algebras distributive laplace pairings and hash products a unified approach to tensor product decompositions of group characters we show for bicommutative graded connected hopf algebras that a certain distributive laplace subgroup of the convolution monoid of 2 cochains parameterizes certain well behaved hopf algebra deformations using the laplace group or its frobenius subgroup we define higher derived hash products and develop a general theory to study their main properties applying our results to the universal bicommutative graded connected hopf algebra of symmetric functions we show that classical tensor product and character decompositions such as those for the general linear group mixed co and contravariant or rational characters orthogonal and symplectic group characters thibon and reduced symmetric group characters are special cases of higher derived hash products in the appendix we discuss a relation to formal group laws

bethe subalgebras in affine birman murakami wenzl algebras and flat connections for q kz equations commutative sets of jucys murphy elements for affine braid groups of types were defined construction of r matrix representations of the affine braid group of type and its distinguished commutative subgroup generated by the type jucys murphy elements are given we describe a general method to produce flat connections for the two boundary quantum knizhnik zamolodchikov equations as necessary conditions for sklyanin s type transfer matrix associated with the two boundary multicomponent zamolodchikov algebra to be invariant under the action of the type jucys murphy elements we specify our general construction to the case of the birman murakami wenzl algebras bmw algebras for short as an application we suggest a baxterization of the dunkl cherednik elements in the double affine hecke algebra of type a

adaptive covariance estimation of locally stationary processes it is shown that the covariance operator of a locally stationary process has approximate eigenvectors that are local cosine functions we model locally stationary processes with pseudo differential operators that are time varying convolutions an adaptive covariance estimation is calculated by searching first for a best local cosine basis which approximates the covariance by a band or a diagonal matrix the estimation is obtained from regularized versions of the diagonal coefficients in the best basis

how much information does dependence between wavelet coefficients contain abstractthis article is motivated by several articles that propose statistical inference where the independence of wavelet coefficients for both short as well as long range dependent time series is assumed we focus on the sample variance and investigate the influence of the dependence between wavelet coefficients and this statistic to this end we derive asymptotic distributional properties of the sample variance for a time series that is synthesized ignoring some or all dependence between wavelet coefficients we show that the second order properties differ from the those of the true time series whose wavelet coefficients have the same marginal distribution except in the independent gaussian case this holds true even if the dependency is correct within each level and only the dependence between levels is ignored in the case of sample autocovariances and sample autocorrelations at lag one we indicate that first order properties are erroneous in a second step we investigate several nonparametric b

boson fermion correspondence for hall littlewood polynomials the boson fermion correspondence is given for the case of the hall littlewood polynomials which is a t deformation of the correspondence realizing the schur polynomials

simultaneous multiple change point and factor analysis for high dimensional time series abstract we propose the first comprehensive treatment of high dimensional time series factor models with multiple change points in their second order structure we operate under the most flexible definition of piecewise stationarity and estimate the number and locations of change points consistently as well as identifying whether they originate in the common or idiosyncratic components through the use of wavelets we transform the problem of change point detection in the second order structure of a high dimensional time series into the relatively easier problem of change point detection in the means of high dimensional panel data also our methodology circumvents the difficult issue of the accurate estimation of the true number of factors in the presence of multiple change points by adopting a screening procedure we further show that consistent factor analysis is achieved over each segment defined by the change points estimated by the proposed methodology in extensive simulation studies we observe that factor analysis prior to change point detection improves the detectability of change points and identify and describe an interesting spillover effect in which substantial breaks in the idiosyncratic components get naturally enough identified as change points in the common components which prompts us to regard the corresponding change points as also acting as a form of factors our methodology is implemented in the r package factorcpt available from cran

locally adaptive estimation of evolutionary wavelet spectra we introduce a wavelet based model of local stationarity this model enlarges the class of locally stationary wavelet processes and contains processes whose spectral density function may change very suddenly in time a notion of time varying wavelet spectrum is uniquely de ned as a wavelet type transform of the autocovariance function with respect to so called autocorrelation wavelets this leads to a natural representation of the autocovariance which is localized on scales we propose a pointwise adaptive estimator of the time varying spectrum the behavior of the estimator studied in homogeneous and inhomogeneous regions of the wavelet spectrum

the littlewood richardson rule and the boson fermion correspondence the boson fermion correspondence is applied to derive explicit formulae for expressing the product of s functions in terms of sums of s functions associated to non standard partitions

twisted vertex representations and spin characters we establish a new group theoretic realization of the basic representations of the twisted affine and twisted toroidal algebras in the same spirit of our new approach to the mckay correspondence our vertex operator construction provides a unified description to the character tables for the spin cover of the wreath product of the twisted hyperoctahedral groups and an arbitrary finite group

bosonic realizations ofuq c 1 n abstract we construct explicitly the quantum symplectic affine algebrauq sp 2n using bosonic fields the fock space decomposes into irreducible modules of level 1 2 quantizing the feingold frenkel construction forq 1

haar fisz estimation of evolutionary wavelet spectra summary we propose a new haar fisz technique for estimating the time varying piecewise constant local variance of a locally stationary gaussian time series we apply our technique to the estimation of the spectral structure in the locally stationary wavelet model our method combines haar wavelets and the variance stabilizing fisz transform the resulting estimator is mean square consistent rapidly computable and easy to implement and performs well in practice we also introduce the haar fisz transform a device for stabilizing the variance of scaled x2 data and bringing their distribution close to gaussianity

equivariant k theory generalized symmetric products and twisted heisenberg algebra for a space x acted on by a finite group the product space xn affords a natural action of the wreath product n n sn the direct sum of equivariant k groups were shown earlier by the author to carry several interesting algebraic structures in this paper we study the k groups of n equivariant clifford supermodules on xn we show that is a hopf algebra and it is isomorphic to the fock space of a twisted heisenberg algebra twisted vertex operators make a natural appearance the algebraic structures on x when is trivial and x is a point specialize to those on a ring of symmetric functions with the schur q functions as a linear basis as a by product we present a novel construction of k theory operations using the spin representations of the hyperoctahedral groups

chern classes of tautological sheaves on hilbert schemes of points on surfaces we give an algorithmic description of the action of the chern classes of tautological bundles on the cohomology of hilbert schemes of points on a smooth surface within the framework of nakajima s oscillator algebra this leads to an identification of the cohomology ring of hilb n a2 with a ring of explicitly given differential operators on a fock space we end with the computation of the top segre classes of tautological bundles associated to line bundles on hilb n up to n 7 extending computations of severi lebarz tikhomirov and troshina and give a conjecture for the generating series

shifted tableaux and the projective representations of symmetric groups les groupes de representation de s n classes de conjugaison algebres de clifford et la representation spin de base produits induits pour des representations spin une application caracteristique pour des caracteres de spin tableaux decales et q fonctions de schur les caracteres de spin irreductibles de s n et a n une analogue decalee de la regle lr produits tensoriels interieurs

a theory for multiresolution signal decomposition the wavelet representation multiresolution representations are effective for analyzing the information content of images the properties of the operator which approximates a signal at a given resolution were studied it is shown that the difference of information between the approximation of a signal at the resolutions 2 sup j 1 and 2 sup j where j is an integer can be extracted by decomposing this signal on a wavelet orthonormal basis of l sup 2 r sup n the vector space of measurable square integrable n dimensional functions in l sup 2 r a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi x this decomposition defines an orthogonal multiresolution representation called a wavelet representation it is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters wavelet representation lies between the spatial and fourier domains for images the wavelet representation differentiates several spatial orientations the application of this representation to data compression in image coding texture discrimination and fractal analysis is discussed