on double centralizer properties between quantum groups and ariki koike algebras abstract in this paper the double centralizer properties for tensor spaces as bimodules over quantum groups and ariki koike algebras as well as their relations with shoji s algebra h h see j algebra 226 2000 818 856 are studied we proved that under the separation condition see j reine angew math 513 1999 53 69 the natural homomorphism from the ariki koike algebra to the endomorphism algebra of tensor space as module over quantum group is surjective we also show that the natural homomorphism from shoji s algebra h h to that endomorphism algebra is always surjective and h h is actually isomorphic to a direct sum of some matrix algebras over some hecke algebras of type a

quantum weyl reciprocity and tilting modules quantum weyl reciprocity relates the representation theory of hecke algebras of type a with that of q schur algebras this paper establishes that weyl reciprocity holds integrally i e over the ring q q 1 of laurent polynomials and that it behaves well under base change a key ingredient in our approach involves the theory of tilting modules for q schur algebras new results obtained in that direction include an explicit determination of the ringel dual algebra of a q schur algebra in all cases in particular in the most interesting situation the ringel dual identifies with a natural quotient algebra of the hecke algebra

on the hyers ulam stability of the functional equations that have the quadratic property abstract the hyers ulam stability of the quadratic functional equation 1 on a restricted domain shall be investigated and the result shall be applied to the study of an asymptotic behavior of that equation furthermore the hyers ulam stability problems of another quadratic equation 4 on a restricted domain shall also be treated under the approximately even or odd condition and some asymptotic behaviors of the quadratic mappings and the additive mappings shall be investigated

marginal models for longitudinal continuous proportional data continuous proportional data arise when the response of interest is a percentage between zero and one e g the percentage of decrease in renal function at different follow up times from the baseline in this paper we propose methods to directly model the marginal means of the longitudinal proportional responses using the simplex distribution of barndorff nielsen and jorgensen that takes into account the fact that such responses are percentages restricted between zero and one and may as well have large dispersion parameters in such a marginal model are estimated using an extended version of the generalized estimating equations where the score vector is a nonlinear function of the observed response the method is illustrated with an ophthalmology study on the use of intraocular gas in retinal repair surgeries

modular representations of hecke algebras of type g p p n hecke algebras for the complex reflection groups g r p n where p 1 and p r were introduced in the work of ariki j algebra 177 1995 164 185 broue and malle asterisque 212 1993 119 189 in this paper we consider modular representation theory for these algebras in the case where r p we assume that the field k contains a primitive pth root of unity e our method is to study the restrictions of specht modules s for hecke algebras hp n of type g p 1 n with parameters q 1 e ep 1 suppose that f q e 0 in k see 4 7 for definition of f q e for any multipartition 1 p of n we prove that s hp p n s k hp p n for any 1 k p 1 where k k 1 k 2 p 1 2 k and if k is the smallest positive integer such that k hence k p we explicitly decompose s hp p n into a direct sum of p k smaller hp p n submodules with the same dimensions as a result when f q e 0 in k we show that hp p n is split over k and get a complete classification of all the absolutely irreducible hp p n modules this generalizes earlier work of c pallikaros j algebra 169 1994 20 48 and j hu manuscripta math 108 2002 409 430 on hecke algebras of type dn which are included as a special case of our main results

schur weyl reciprocity for ariki koike algebras let g glm1 glmr be a levi subalgebra of glm with m ri 1mi and v the natural representation of the quantum group uq g we construct a representation of the ariki koike algebra hn r on the n fold tensor space of v commuting with the action of uq g and prove the schur weyl reciprocity for the actions of uq g and hn r on it

the schur algebra we study a class of endomomorphism algebras of certain q permutation modules over the hecke algebra of type b whose summands involve both parabolic and quasi parabolic subgroups and prove that these algebras are integrally free and quasi hereditary and are stable under base change some consequences for decomposition numbers are discussed the notion of a q schur algebra was introduced by dipper and james dj2 who used these algebras to parametrize the irreducible representations of the finite general linear groups in non describing characteristics with hindsight these algebras had already appeared earlier in an entirely different quantum group context ji inspired by physics in ji jimbo considered the endomorphism algebras of tensor spaces as hecke algebra modules in his context a q schur algebra can be viewed as a quotient of the quantized enveloping algebra associated to gln in pw these algebras were shown to be quasi hereditary the quasi heredity property is an embodiment in classical algebra of the geometric derived category stratification exhibited by perverse sheaves ps it means more applications can be deduced from a ring theoretic point of view see e g dps3 and the possibility is raised of even deeper results in the future as suggested by cps2 certainly these algebras play a central role in the representation theories of the finite and quantum general linear groups naturally one asks are there such algebras for types other than a our paper ds showed that there were similar quasi hereditary quotients of quantized enveloping algebras for all types of root systems however no connection with hecke algebras and finite groups of lie type was found there this paper aims at the same question and constructs possible algebras directly from hecke algebras hence from finite groups of lie type we restrict attention to the type b case imitating the definition of a q schur algebra we introduce the notion of a q schur algebra these algebras are the endomorphism algebras of certain modules over the hecke algebra of type b called tensor spaces whose summands involve not only parabolic subgroups but also quasi parabolic subgroups of the weyl group of type b a main result of our paper shows that qschur algebras are quasi hereditary we speculate that similar constructions exist for other classical types only type d remains actually since type c is equivalent received by the editors march 3 1997 and in revised form october 28 1998 2000 mathematics subject classification primary 20c08 20g05 20c33 the authors would like to thank arc for support under the large grant a69530243 as well as nsf and the universities of virginia and new south wales for their cooperation the first author also thanks the newton institute at cambridge for its hospitality c 2000 american mathematical society

on the decomposition numbers of the hecke algebra of type dn when n is even abstract let n 4 be an even integer let k be a field with char k 2 and q an invertible element in k such that i 1 n 1 1 q i 0 in this paper we study the decomposition numbers over k of the iwahori hecke algebra h q d n of type d n we obtain some equalities which relate its decomposition numbers with certain schur elements and the decomposition numbers of various iwahori hecke algebras of type a with the same parameter q when char k 0 this completely determine all of its decomposition numbers the main tools we used are the morita equivalence theorem established in j hu a morita equivalence theorem for hecke algebra h q d n when n is even manuscripta math 108 2002 409 430 and certain twining character formulae of weyl modules over a tensor product of two q schur algebras

a partially linear additive model for clustered proportion data proportion data with support lying in the interval 0 1 are a commonplace in various domains of medicine and public health when these data are available as clusters it is important to correctly incorporate the within cluster correlation to improve the estimation efficiency while conducting regression based risk evaluation furthermore covariates may exhibit a nonlinear relationship with the proportion responses while quantifying disease status as an alternative to various existing classical methods for modeling proportion data such as augmented beta regression that uses maximum likelihood or generalized estimating equations we develop a partially linear additive model based on the quadratic inference function relying on quasi likelihood estimation techniques and polynomial spline approximation for unknown nonparametric functions we obtain the estimators for both parametric part and nonparametric part of our model and study their large sample theoretical properties we illustrate the advantages and usefulness of our proposition over other alternatives via extensive simulation studies and application to a real dataset from a clinical periodontal study

q tensor space and q weyl modules we obtain the irreducible representations of the q schur algebra motivated by the fact that these representations give all the irreducible representations of gln q in the nondescribing characteristic the irreducible polynomial representations of the general linear groups in the describing characteristic are a special case of this construction the theory of polynomial representations of general linear groups is equivalent to the representation theory of schur algebras see green s book 5 and the bibliography therein in 4 we defined q analogues of schur algebras when q 1 these are the usual schur algebras and when q is a prime power representations of q schur algebras give a substantial part of the representation theory of finite general linear groups in the nondescribing characteristic case including all irreducible representations of these groups and important information about decomposition numbers it is natural to ask what features of the classical schur algebras have qanalogues in this paper we define q analogues of tensor space of weyl modules and of weight spaces thereby generalizing the main reslllts which appear in green s book 5 for example we classify the irreducible modules for qschur algebras we determine bases for q weyl modules compatible with weight spaces and we give results on composition multiplicities of the irreducible modules in q weyl modules the proofs are largely self contained so by specializing q to 1 we recover the corresponding results in 5 this paper therefore is relevant to the representation theory of symmetric groups and to the representation theory of general linear groups in the describing and in the nondescribing characteristics 1 the q schur algebra let r be a natural number let r be an integral domain and let q be a unit in r we denote the symmetric group on r letters by er the hecke algebra z is the r free r algebra with basis twlw e er where the multiplication is determined by the following rule if a i i 1 is a basic transposition in received by the editors august 15 1989 1980 mathematics subject classification 198 5 revision primary 1 6a64 1 6a6 5 secondary 20c30 this research was supported in part by nsf grant no dms 8802290 the authors gratefully acknowledge support received from nato grant no 0222 87 r 1991 american mathematical society 0002 9947 91 1 00 25 per page

a generalization of the hyers ulam rassias stability of jensen s equation in this paper we prove a generalization of the stability of the jensen s equation in the spirit of hyers ulam rassias and g vruta

profile kernel versus backfitting in the partially linear models for longitudinal clustered data summary we study the profile kernel and backfitting methods in partially linear models for clustered longitudinal data for independent data despite the potential root n inconsist ency of the backfitting estimator noted by rice 1986 the two estimators have the same asymptotic variance matrix as shown by opsomer ruppert 1999 in this paper theoretical comparisons of the two estimators for multivariate responses are investigated we show that for correlated data backfitting often produces a larger asymptotic variance than the profile kernel method that is for clustered data in addition to its bias problem the backfitting estimator does not have the same asymptotic efficiency as the profile kernel estimator consequently the common practice of using the backfitting method to compute profile kernel estimates is no longer advised we illustrate this in detail by following zeger diggle 1994 and lin carroll 2001 with a working independence covariance structure for nonparametric estimation and a correlated covariance structure for para metric estimation numerical performance of the two estimators is investigated through a simulation study their application to an ophthalmology dataset is also described

correlated binary regression with covariates specific to each binary observation regression methods are considered for the analysis of correlated binary data when each binary observation may have its own covariates it is argued that binary response models that condition on some or all binary responses in a given block are useful for studying certain types of dependencies but not for the estimation of marginal response probabilities or pairwise correlations fully parametric approaches to these latter problems appear to be unduly complicated except in such special cases as the analysis of paired binary data hence a generalized estimating equation approach is advocated for inference on response probabilities and correlations illustrations involving both small and large block sizes are provided

rational cherednik algebras and hilbert schemes let h c be the rational cherednik algebra of type a n 1 with spherical subalgebra u c e h c e then u c is filtered by order of differential operators with associated graded ring mbox gr u c mathbb c mathfrak h oplus mathfrak h where w is the n th symmetric group we construct a filtered mathbb z algebra b such that under mild conditions on c the category b qgr of graded noetherian b modules modulo torsion is equivalent to u c mod the associated graded mathbb z algebra mbox gr b has mbox gr b lqgr simeq coh hilb n this can be regarded as saying that u c simultaneously gives a non commutative deformation of mathfrak h oplus mathfrak h w and of its resolution of singularities hilb n rightarrow mathfrak h oplus mathfrak h as we show elsewhere this result is a powerful tool for studying the representation theory of h c and its relationship to hilb n

hyperoctahedral schur algebras we study the centralising algebra of a natural action of the hyperoctahedral group i e a finite weyl group of typebr on ther th tensor power of a2n dimensional space the centralising algebra of this is shown to have a product rule similar to schur s product rule in typea we deform this action to an action of the hecke algebra of typeband study the associated centralising algebra of typeband its dual we introduce and studyq permutation modules for the algebra

on tensor spaces over hecke algebras of type bn abstract let w b n be the weyl group of type b n and h b n be the associated iwahori hecke algebra in this paper we study the n tensor space v n where dim v 2 m with natural actions introduced in r m green hyperoctahedral schur algebras j algebra 192 1997 418 438 of w b n and of h b n for each composition 1 m of n let e be the corresponding initial basis element of v n see 3 8 for definition we show that if d is a distinguished right coset representative of s in w b n then the action of the natural basis element t d on e coincides with the permutation action of d up to a scalar as an application we prove that the n tensor space decomposes at the integral level into a direct sum of some permutation modules over hecke algebra h b n with respect to certain standard parabolic subalgebras

on the hyers ulam rassias stability of functional equations in n variables abstract in this paper we investigate a generalization of the hyers ulam rassias stability for a functional equation of the form f x x f x x and the stability in the sense of ger for the functional equation of the form f x x f x where x lie in n variables as a consequence we obtain a stability result in the sense of hyers ulam rassias g vruta and ger for some well known equations such as the gamma beta and g function type s equations

generalization of functional equation for the square root spiral abstract in the paper we give the general solution of the linear functional equation p 1 p x c x h x furthermore we discuss its hyers ulam rassias stability and the stability in the sense of ger for the equation p 1 p x c x our results are applied to the square root spiral so that the related results by heuvers et al k j heuvers d s moak b boursaw the functional equation of the square root spiral in th m rassias ed functional equations and inequalities kluwer 2000 pp 111 117 and results by jung and sahoo stability of functional equation for square root spirals appl math lett 15 2002 435 438 are generalized

the analysis of binary longitudinal data with time independent covariates summary this paper considers extensions of logistic regression to the case where the binary outcome variable is observed repeatedly for each subject we propose two working models that lead to consistent estimates of the regression parameters and of their variances under mild assumptions about the time dependence within each subject s data the efficiency of the proposed estimators is examined an analysis of stress in mothers with infants is presented to illustrate the proposed method

quasi parabolic subgroups of g m 1 r abstract we study the properties of cosets and double cosets of quasi parabolic subgroups via tableaux we characterize these double cosets by n n arrays of non negative integer sequences for each double coset we construct and count all shortest and longest representatives and find their lengths we also find the number of double cosets in g m 1 r of each pair of quasi parabolic subgroups

a generalized partially linear mean covariance regression model for longitudinal proportional data with applications to the analysis of quality of life data from cancer clinical trials motivated by the analysis of quality of life data from a clinical trial on early breast cancer we propose in this paper a generalized partially linear mean covariance regression model for longitudinal proportional data which are bounded in a closed interval cholesky decomposition of the covariance matrix for within subject responses and generalized estimation equations are used to estimate unknown parameters and the nonlinear function in the model simulation studies are performed to evaluate the performance of the proposed estimation procedures our new model is also applied to analyze the data from the cancer clinical trial that motivated this research in comparison with available models in the literature the proposed model does not require specific parametric assumptions on the density function of the longitudinal responses and the probability function of the boundary values and can capture dynamic changes of time or other interested variables on both mean and covariance of the correlated proportional responses copyright 2017 john wiley sons ltd

on the hyers ulam rassias stability of a quadratic functional equation abstract in this paper we investigate the hyers ulam rassias stability problems of a new quadratic functional equation f x y z f x f y f z f x y f y z f z x furthermore the stability results will be applied to the study of an interesting asymptotic property of the quadratic functions

stability of functional equations in single variable abstract this paper discusses hyers ulam stability for functional equations in single variable including the forms of linear functional equation nonlinear functional equation and iterative equation surveying many known and related results we clarify the relations between hyers ulam stability and other senses of stability such as iterative stability continuous dependence and robust stability which are used for functional equations applying results of nonlinear functional equations we give the hyers ulam stability of bottcher s equation we also prove a general result of hyers ulam stability for iterative equations

multivariate regression analyses for categorical data summary it is common to observe a vector of discrete and or continuous responses in scientific problems where the objective is to characterize the dependence of each response on explanatory variables and to account for the association between the outcomes the response vector can comprise repeated observations on one variable as in longitudinal studies or genetic studies of families or can include observations for different variables this paper discusses a class of models for the marginal expectations of each response and for pairwise associations the marginal models are contrasted with log linear models two generalized estimating equation approaches are compared for parameter estimation the first focuses on the regression parameters the second simultaneously estimates the regression and association parameters the robustness and efficiency of each is discussed the methods are illustrated with analyses of two data sets from public health research

longitudinal data analysis using generalized linear models summary this paper proposes an extension of generalized linear models to the analysis of longitudinal data we introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence the estimating equations are derived without specifying the joint distribution of a subject s observations yet they reduce to the score equations for multivariate gaussian outcomes asymptotic theory is presented for the general class of estimators specific cases in which we assume independence m dependence and exchangeable correlation structures from each subject are discussed efficiency of the proposed estimators in two simple situations is considered the approach is closely related to quasi likelih ood some key ironh estimating equation generalized linear model longitudinal data quasi likelihood repeated measures

augmented mixed beta regression models for periodontal proportion data continuous clustered proportion data often arise in various domains of medicine and public health where the response variable of interest is a proportion or percentage quantifying disease status for the cluster units ranging between zero and one however because of the presence of relatively disease free as well as heavily diseased subjects in any study the proportion values can lie in the interval 0 1 while beta regression can be adapted to assess covariate effects in these situations its versatility is often challenged because of the presence excess of zeros and ones because the beta support lies in the interval 0 1 to circumvent this we augment the probabilities of zero and one with the beta density controlling for the clustering effect our approach is bayesian with the ability to borrow information across various stages of the complex model hierarchy and produces a computationally convenient framework amenable to available freeware the marginal likelihood is tractable and can be used to develop bayesian case deletion influence diagnostics based on q divergence measures both simulation studies and application to a real dataset from a clinical periodontology study quantify the gain in model fit and parameter estimation over other ad hoc alternatives and provide quantitative insight into assessing the true covariate effects on the proportion responses

the affineq schur algebra abstract we introduce an analogue of the q schur algebra associated to coxeter systems of type a n 1 we give two constructions of this algebra the first construction realizes the algebra as a certain endomorphism algebra arising from an affine hecke algebra of type a r 1 where n r this generalizes the original q schur algebra as defined by dipper and james and the new algebra contains the ordinary q schur algebra and the affine hecke algebra as subalgebras using this approach we can prove a double centralizer property the second construction realizes the affine q schur algebra as the faithful quotient of the action of a quantum group on the tensor power of a certain module analogous to the construction of the ordinary q schur algebra as a quotient of u g l n