finite resolutions of modules for reductive algebraic groups of a suitable g module m by modules which are required to be direct sums of tensor products of exterior powers of the natural representation in particular in z 31 for partitions 1 and p resolutions are constructed for the modules l f and l f the schur functor corresponding to 1 and the skew schur functor corresponding to a p evaluated at f where f is a free module over a field or the integers the purpose of this paper is to characterise the gl modules which admit such a resolution as those modules which have a filtration in which each successive quotient has the form l f for some partition p by contrast with 2 3 we do not produce resolutions explicitly our methods are independent of those of akin and buchsbaum we give a new proof of their result on the existence of a resolution for l f and are algebraic group theoretic in nature we have therefore cast our main result the theorem of section 1 as a statement about resolutions for reductive algebraic groups over an algebraically closed field one may frequently wish to work over a more general coefficient ring see l 3 and so we treat in some detail chevalley group schemes and general linear group schemes over a principal ideal domain 2 6 and 2 7 giving the appropriate versions of our main result and relating it to the work of akin buchsbaum and weyman

design of iir digital filters in the complex domain by transforming the desired response in this paper we present a new design method of infinite impulse response iir digital filters with quasi equiripple absolute error in the complex domain this method is based on solving a least squares solution iteratively at each iteration the desired response for the least squares approximation is transformed to have equiripple error this algorithm is efficient because there is no need for any initial value or complex optimization algorithm by this method a quasi equiripple solution is obtained very quickly with less computational complexity moreover by multiplying an arbitrary weighting function on the desired responses of passband and stopband respectively the error at the passband and stopband can be controlled finally we show some examples to validate the proposed method

skew modules for reductive groups skew modules for symmetric groups have been investigated by james and peel 13 farahat and peel 9 and clausen s more recently skew modules for general linear groups have been investigated by akin buchsbaum weyman 3 l 2 and kouwenhoven 161 our aim in this paper is to set up in a rather general context a theory of skew modules for reductive algebraic groups for a partition 1 of it james peel 13 obtain a filtration of the specht module sj viewed as a module for the young subgroup corresponding to a decomposition n a b of n the successive quotients in the filtration have the form s h sj p kronecker product where p runs over the partitions of a such that p is a skew partition and s denotes the skew specht module the analogue of this result is proved for general linear groups by akin buchsbaum and weyman 3 theorem 11 4 1 l and kouwenhoven 16 proposition ii 2 2a the analogue for reductive groups is more or less our definition of skew modules this filtration property is in fact a characterisation of skew modules see 1 3 4 and our definition for general linear groups therefore agrees with that of akin buchsbaum and weyman 3 and kouwenhoven 161 it becomes apparent rather quickly from our point of view that the skew modules have a particular kind of filtration see 2 1 1 which in the case of the general linear group is a filtration by schur modules this is a result of kouwenhoven 16 proposition 11 2 2b a for general linear groups kouwenhoven is able to give an explicit description of such a filtration one may then obtain as in kouwenhoven 16 proposition ii 2 2b b the result of james and peel 131 on the existence of specht series for skew modules for the symmetric groups by specializing to a certain weight space i e applying the schur functor as in ll chap 63 we are also able to prove see 2 3 3 the existence of a certain kind of resolution considered by akin and buchsbaum see 1 sects 83 for skew modules for general linear groups our main point of reference is the representation theory of reductive 465 0021 8693 88 3 00

a general chebyshev complex function approximation procedure and an application to beamforming a new computational technique is described for the chebyshev or minimax approximation of a given complex valued function by means of linear combinations of given complex valued basis functions the domain of definition of all functions can be any finite set whatever neither the basis functions nor the function approximated need satisfy any special hypotheses beyond the requirement that they be defined on a common domain theoretical upper and lower bounds on the accuracy of the computed chebyshev error are derived these bounds permit both a priori and a posteriori error assessments efforts to extend the method to functions whose domain of definition is a continuum are discussed an application is presented involving re shading a 50 element antenna array to minimize the effects of a 10 element failure rate while maintaining full steering capability and mainlobe beamwidth

characteristic free representation theory of the general linear group ii homological considerations in our first paper of this series cl we indicated how we were led to consider resolutions of schur and weyl modules of a particular form in order to prove the existence of these resolutions we were forced to enlarge the family of skew shapes to a class j containing new shapes whose corresponding schur and weyl modules had heretofore not been studied with these shapes in hand we proved in 1 the existence of some fundamental exact sequences and described how from these exact sequences we could use a mapping cone construction to build up the resolutions we were seeking for this mapping cone construction we needed maps and to provide maps we needed projectivity of tensor products of divided powers this led to the study of the schur algebra and its decomposition into orthogonal idempotents in sections 1 and 2 we review the information about the schur algebra that we need to carry out our program fortunately there is a very clear and detailed exposition of this subject in the notes of j a green s from which we borrowed very heavily in fact the main function of the first two sections is to condense and translate into our notation and terminology the relevant sections of green s notes in sections 3 and 4 we define the family of shapes j that we will study

resolutions of determinantal ideals the submaximal minors for many years there has been considerable interest in finding a resolution of the ideal generated by the minors of order p of a generic m x n matrix to put the problem more precisely suppose r is a commutative ring and x are variables with 1 i m and 1 j q n if we let r r x be the polynomial ring over r then we have the generic matrix x and we may form the ideal zp in r generated by the p x p minors of this matrix the problem then is to find an explicit free resolution of the ideal zp over the ring r it was proved by eagon and hochster lo that r i has a resolution of length m p l n p l but their proof consisted in showing that the ideal zp is perfect it did not provide a construction of the resolution in fact it is not known whether the betti numbers of the ideal zp depend on the characteristic of the ground ring r in 121 lascoux succeeded in giving an explicit resolution provided that the ground ring r contained the field q of rational numbers his construction rests heavily on the theory of schur functors and the fact that in characteristic zero the schur functors are the irreducible representations of the general linear group over the integers however the construction breaks down despite the fact that one can define the schur functors over an arbitrary commutative ring see 1 2 14 151 for various constructions of schur functors in analyzing the work of lascoux and its subsequent reworking by nielsen 131 some basic facts seemed to clamor for attention one was that within a resolution of r z there appeared to be two types of boundary maps one of degree 1 and one of degree p the maps of degree 1 were maps between sums of schur functors of fixed durfee square k see section 2 for definitions while the maps of degree p were from sums of schur functors of

extensions of symmetric tensors by alternating tensors on demontre que les groupes d extension des tenseurs symetriques par des tenseurs alternes sont determines par les composantes homogenes des modules d homologie de l hyperalgebre du groupe additif g a

design of fir digital phase networks the problem of the minimax design of fir digital filters with prescribed phase characteristics and unit magnitude is a nonlinear optimization problem in this paper it is approximated by a linear programming problem and it is shown that the solution of this linear program is optimal to first order that is if 0 and e 0 are optimal deviations of magnitude and phase characteristics then the actual deviations obtained from the linear program solution satisfy delta leq delta 0 epsilon min 0 max 2 and epsilon leq epsilon 0 1 delta 0 1 delta 0 numerical examples are given including design results for full band m term chirp filters which like linear phase filters can be implemented with m 1 2 multiplications per point

intertwining numbers the three rowed case a standard question in modular representation theory is what is the i zr p dimension of the zr p vector space ext k k the bars over a l m r the modules indicate the reduction of these modules modulo p the other notation is explained below these numbers are called intertwining numbers the attempts to determine these intertwining numbers are varied one approach is suggested by the following special case of a theorem found in w x ab1

a short proof of a theorem of m hashimoto abstract recently m hashimoto announced that the resolutions of determinantal ideals depend on the characteristic of the base field the purpose of this note is to give a short proof of this result one should stress that even though the method we use is different from hashimoto s his result provided us with the clue where the additional relation exists

schur de rham complex and its cohomology abstract we associate to a young diagram the schur de rham complex s we show that this complex is exact when the p core of is nontrivial and compute its cohomology when the p core is trivial and the p quotient of consists of a single diagram

on the ext groups between weyl modules for gln abstract this paper studies extension groups between certain weyl modules for the algebraic group gl n over the integers main results include 1 a complete determination of ext groups between weyl modules whose highest weights differ by a single root and 2 determination of ext 1 between an exterior power of the defining representation and any weyl module the significance of these results for modular representation theory of gl n is discussed in several remarks notably the first result leads to a calculation of ext groups between neighboring weyl modules for gl n and also recovers the gl n case of a recent result of andersen some generalities about ext groups between weyl modules and a brief overview of known results about these groups are also included

characteristic free representation theory of the general linear group on etudie systematiquement les z formes des representations rationnelles du groupe lineaire generale

weighted least squares design and characterization of complex fir filters the paper presents two novel weighted least squares methods for the design of complex coefficient finite impulse response fir filters to attain specified arbitrary multiband magnitude and linear or arbitrary phase responses these methods are computationally efficient requiring only the solution of a toeplitz system of n linear equations for an n length filter that can be obtained in o n sup 2 operations illustrative filter design examples are presented

a note on the semi infinite programming approach to complex approximation several observations are made about a recently proposed semi infinite programming sip method for computation of linear chebyshev approximations to complex valued func tions a particular discretization of the sip problem is shown to be equivalent to replacing the usual absolute value of a complex number with related estimates resulting in a class of quasi norms on the complex number field c and consequently a class of quasi norms on the space c q consisting of all continuous functions defined on q c c q compact these quasi norms on c q are estimates of the loo norm on c q and are useful because the best approximation problem in each quasi norm can be solved by solving i an ordinary linear program if q is finite or ii a simplified sip if q is not finite glashoff and roleff 1 solve a semi infinite program sip which is shown to be equivalent to the linear approximation problem for functions in c q where c q is the space of complex valued continuous functions on a compact and not necessarily finite subset q of the complex plane c and is equipped with the uniform lo norm

approximation of fir by iir digital filters an algorithm based on balanced model reduction an algorithm for the approximation of finite impulse response fir filters by infinite impulse response iir filters is presented the algorithm is based on a concept of balanced model reduction the matrix inversions normally associated with this procedure are notoriously error prone due to ill conditioning of the special matrix forms required this difficulty is circumvented here by directly formulating a reduced state space system description which is input output equivalent to the system that would more conventionally be obtained following the explicit step of constructing an interim balanced realization examples of fir by iir filter approximations are included

digital filters with equiripple magnitude and group delay this paper introduces a class of recursive digital filters having equiripple behavior in both the magnitude and group delay responses the filters consist of an all pole iir component cascaded with a linear phase fir component the iir component is synthesized so that its group delay exhibits an equiripple variation in the passband whereas the fir component is used to obtain the desired equiripple nature for the amplitude response in both the passband and stopband s an iterative procedure is presented for optimizing the ripple in the group delay and the order of the iir part in such a way that the overall multiplication rate attains its minimum examples show that standard simultaneous amplitude and phase optimization methods only slightly change the results obtained using this method the new method is straightforward to implement and avoids the problems of guessing good initial values and of premature termination several examples show that the new filters require significantly fewer multipliers in narrow band applications than equivalent fir and delay equalized elliptic designs at the expense of a negligible variation in the group delay

a new method for chebyshev approximation of complex valued functions problems of this type appear in many connections and have been treated by various authors cf 2 12 13 considering the computation of best rational chebyshev approximations to complex valued functions by descent algorithms ellacott and williams 6 report that the main portion of computer time is spent in the solution of the linear subproblems they have applied the very slowly convergent lawson algorithm to these subproblems and they remark that a fast linear algorithm would bring about a significant improvement in efficiency in our paper we describe a new algorithm which seems to be the first one which works for the continuous case where t is not a finite set too in our method we transform the complex approximation problem into a real linear optimization problem with infinitely many constraints a so called semi infinite program sip cf 5 8 10 this is solved by a two step procedure in the first step we apply the stabilized simplex algorithm to a discrete approximation of the sip and in the second we make use of the newton raphson method in order to obtain very rapidly the solution of the sip and thus of our original approximation problem

markov chain monte carlo methods for stochastic volatility models this paper is concerned with simulation based inference in generalized models of stochastic volatility defined by heavy tailed student t distributions with unknown degrees of freedom and exogenous variables in the observation and volatility equations and a jump component in the observation equation by building on the work of kim shephard and chib rev econom stud 65 1998 361 we develop efficient markov chain monte carlo algorithms for estimating these models the paper also discusses how the likelihood function of these models can be computed by appropriate particle filter methods computation of the marginal likelihood by the method of chib j amer statist assoc 90 1995 1313 is also considered the methodology is extensively tested and validated on simulated data and then applied in detail to daily returns data on the s p 500 index where several stochastic volatility models are formally compared under different priors on the parameters

the caratheodory fejer method for recursive digital filter design a new technique for rational digital filter design is presented which is based on results in complex function theory due to takagi krein and others starting from a truncated or windowed impulse response the method computes the unique optimum rational chebyshev approximation with a prescribed number of stable poles both phase and magnitude are matched deleting the noncausal unstable part of the chebyshev approximation yields a stable approximation of specified order m n which is close to optimal in the chebyshev sense no iteration is involved except in the determination of an eigenvalue and eigenvector of the hankel matrix of impulse response coefficients in this paper the algorithm is specified and practical examples are discussed

permutation resolutions for specht modules of hecke algebras abstract in boltje and hartmann 2011 bh a chain complex was constructed in a combinatorial way which conjecturally is a resolution of the dual of the integral specht module for the symmetric group in terms of permutation modules in this paper we extend the definition of the chain complex to the integral iwahori hecke algebra and prove the same partial exactness results that were proven in the symmetric group case

a straightening algorithm for row convex tableaux abstract we produce a new basis for the schur and weyl modules associated to a row convex shape d the basis is indexed by a new class of straight tableaux which we introduce by weakening the usual requirements for standard tableaux spanning is proved via a new straightening algorithm for expanding elements of the representation into this basis for skew shapes this algorithm specializes to the classical straightening law the new straight basis is used to produce bases for flagged schur and weyl modules to provide groebner and sagbi bases for the homogeneous coordinate rings of some configuration varieties and to produce a flagged branching rule for row convex representations systematic use of supersymmetric letterplace techniques enables the representation theoretic results to be applied to representations of the general linear lie superalgebra as well as to the general linear group

comments on design of iir filters in the complex domain by x chen and t w parks in commenting on the above namework see ibid vol 38 no 6 p 910 20 1990 it is shown how good starting values can be obtained for the minimax design of infinite impulse response iir digital filters in the complex domain with the ellacott williams 1976 1979 algorithm

addendum specht modules for column convex diagrams characteristic free results for weyl modules abstract it is shown that the results in reiner and shimozono 12 have characteristic free analogues for weyl modules

design of fir filters in the complex domain the design of fir digital filters with a complex valued desired frequency response using the chebyshev error is investigated the complex approximation problem is converted into a real approximation problem which is nearly equivalent to the complex problem a standard linear programming algorithm for the chebyshev solution of overdetermined equations is used to solve the real approximation problem additional constraints are introduced which allow weighting of the phase and or group delay of the approximation digital filters are designed which have nearly constant group delay in the passbands the desired constant group delay which gives the minimum chebyshev error is found to be smaller than that of a linear phase filter of the same length these filters in addition to having a smaller approximately constant group delay have better magnitude characteristics than exactly linear phase filters with the same length the filters have nearly equiripple magnitude and group delay

on schur algebras and related algebras ii this paper is a continuation of 7 the purpose of 7 was to set up in the context of reductive algebraic groups a theory of generalized schur algebras a special case of our construction gives the schur algebras s n r studied extensively in lo we concentrate here on the schur algebras themselves and show that our construction yields new results in their representation theory by means of the schur functor see 10 chap 6 we obtain new results in the representation theory of the symmetric groups the main results are as follows the schur algebras s n r defined over a principal ideal domain r have finite global dimension see also 1 i over a field or complete valuation ring r every finitely generated projective s n r module has a weyl module filtration we prove the irreducibility of the socle of certain weyl modules see also 15 we describe a connection between weights of projective indecomposable modules for the schur algebras in terms of the involution on irreducible representations of symmetric groups given by tensoring with the sign representation we show that over a complete valuation ring or a field every young module for a symmetric group has a specht series in particular the projective indecomposables have specht series finally we show that for r n and a complete valuation ring or field r the blocks of the schur algebra s n r are given by the rule embodied in nakayama s conjecture the notations and conventions are as in the first part of this work 7

optimal prediction pools a prediction model is any statement of a probability distribution for an outcome not yet observed this study considers the properties of weighted linear combinations of n prediction models or linear pools evaluated using the conventional log predictive scoring rule the log score is a concave function of the weights and in general an optimal linear combination will include several models with positive weights despite the fact that exactly one model has limiting posterior probability one the paper derives several interesting formal results for example a prediction model with positive weight in a pool may have zero weight if some other models are deleted from that pool the results are illustrated using s p 500 returns with prediction models from the arch stochastic volatility and markov mixture families in this example models that are clearly inferior by the usual scoring criteria have positive weights in optimal linear pools and these pools substantially outperform their best components

simultaneous design in both magnitude and group delay of iir and fir filters based on multiple criterion optimization this work considers the simultaneous design in both magnitude and group delay of digital transfer functions on the basis of multiple criterion optimization both causal iir filters and nonlinear phase fir filters are studied examples of the optimal tradeoff filters both fir filters and iir filters are presented and their characteristics are analyzed

skew weyl modules for gln and degree reduction for schur algebras abstract we prove a strong characteristic free analogue of the classical adjoint formula s s f s f in the ring of symmetric functions this is done by showing that the representative of a suitably chosen functor involving a tensor product is the skew weyl module by strong we mean that this representative preserves not only hom groups but higher ext groups also a fact which can be used to compute some homological invariants of weyl modules for gln via recursion on degree we use the following main tools existence of weyl filtrations in tensor products of weyl modules the akin buchsbaum weyman constructions of weyl modules and certain vanishing properties of ext groups

schur modules weyl modules and capelli operators much work has been done in recent years towards presenting explicitly and with a minimum of machinery the irreducible representations of the general linear group gl n over a field k the representations obtained from the modules named after schur and weyl have undergone a tortuous refining process in the hands of notable authors akin buchsbaum and weyman 1 2 carter and lusztig 7 clausen 8 9 de concini eisenbud and procesi 10 green 16 james and kerber 19 towber 26 27 in the wake of the pioneering work of schur 23 and weyl 28 one objective of such simplifications has been that of obtaining information as to the reducibility of representations when the field k if of positive characteristic an objective which seems as yet out of reach the purpose of this work is that of organically presenting the main results on schur and weyl modules our techniques are at variance with most of those previously used and we should like to believe our proofs signify a return to the primordial combinatorial underpinning of the topic we hope thereby to have attained a maximum of characteristic freeness our two warhorses are 1 the well known straightening technique first used by doubilet rota and stein 15 and recently generalized to the supersymmetric case by grosshans rota and stein 17 an altogether different approach from which we have also benefitted has been developed by akin buchsbaum and weyman 1 both techniques has been skillfully displayed in the recent work of kouwenhoven 21 2 the use of polarization operators combined with the striking power of kostant s z form 20 in the guise of de sarme nien kung and rota s capelli operators 13 superalgebraic methods are used in obtaining two distinct standard basis theorems for the case of the exterior letterplace algebra such an algebra with its straightening possibilities was first considered by doubilet and rota 14 and then brought to fruish by akin buchsbaum and weyman 1 by these methods we derive what is perhaps the main novelty of the doi 10 1006 aima 1999 1872 available online at http www idealibrary com on

incorporating overnight and intraday returns into multivariate garch volatility models abstract we propose and evaluate mixed frequency multivariate garch models for forecasting low frequency weekly volatility based on high frequency intraday returns at 5 minute intervals and on the overnight returns the low frequency conditional volatility matrix is modeled as a weighted sum of an intraday and an overnight component the components are specified as multivariate garch processes of the bekk type adapted to the mixed frequency data setting and may enter the model as two separate components or as a single one the models may further be extended by a nonparametrically estimated slowly varying long run volatility matrix we evaluate the models in and out of sample using the 5 minute and overnight returns on four djia stocks axp ge hd and ibm from january 1988 to november 2014 and find that they systematically dominate a variety of models that only use lower frequency data weekly daily or close to open and open to close returns

design of stable iir filters in the complex domain by automatic delay selection a major problem encountered when designing infinite impulse response iir filters in the complex domain is to ensure that the filter is stable instability occurs frequently when the iir filter approximates the inverse of a nonminimum phase system this is often the case for equalization filters addition of delay to the target frequency response can result in a stable filter however to date delay selection has been a matter of trial and error the article presents an automated method for finding the delay

characteristic free resolutions of weyl and specht modules abstract we construct explicit resolutions of weyl modules by divided powers and of co specht modules by permutational modules we also prove a conjecture by boltje and hartmann 2010 7 on resolutions of co specht modules

least squares design of iir filters with prescribed magnitude and phase responses and a pole radius constraint this paper presents a method for the frequency domain design of infinite impulse response iir digital filters the proposed method designs filters approximating prescribed magnitude and phase responses iir filters of this kind can have approximately linear phase responses in their passbands or they can equalize magnitude and phase responses of given systems in many cases these filters can be implemented with less memory and with fewer computations per output sample than equivalent finite impulse response fir digital filters an important feature of the proposed method is the possibility to specify a maximum radius for the poles of the designed rational transfer function consequently stability can be guaranteed and undesired effects of implementations using fixed point arithmetic can be alleviated by restricting the poles to keep a prescribed distance from the unit circle this is achieved by applying rouche s theorem in the proposed design algorithm we motivate the use of iir filters with an unequal number of poles and zeros outside the origin of the complex plane in order to satisfy simultaneous specifications on magnitude and phase responses it is advantageous to use iir filters with only a few poles outside the origin of the z plane and an arbitrary number of zeros filters of this type are a compromise between iir filters with optimum magnitude responses and phase approximating fir filters we use design examples to compare filters designed by the proposed method to those obtained by other methods in addition we compare the proposed general iir filters with other popular more specialized structures such as fir filters and cascaded systems consisting of frequency selective iir filters and phase equalizing allpass filters

strictly proper scoring rules prediction and estimation scoring rules assess the quality of probabilistic forecasts by assigning a numerical score based on the predictive distribution and on the event or value that materializes a scoring rule is proper if the forecaster maximizes the expected score for an observation drawn from the distributionf if he or she issues the probabilistic forecast f rather than g f it is strictly proper if the maximum is unique in prediction problems proper scoring rules encourage the forecaster to make careful assessments and to be honest in estimation problems strictly proper scoring rules provide attractive loss and utility functions that can be tailored to the problem at hand this article reviews and develops the theory of proper scoring rules on general probability spaces and proposes and discusses examples thereof proper scoring rules derive from convex functions and relate to information measures entropy functions and bregman divergences in the case of categorical variables we prove a rigorous version of the

a wise method for designing iir filters the problem of designing optimal digital iir filters with frequency responses approximating arbitrarily chosen complex functions is considered the real valued coefficients of the filter s transfer function are obtained by numerical minimization of carefully formulated cost which is referred here to as the weighted integral of the squared error wise criterion the wise criterion linearly combines the wls criterion that is used in the weighted least squares approach toward filter design and some time domain components the wls part of wise enforces the quality of the frequency response of the designed filter while the time domain part of the wise criterion restricts the positions of the filter s poles to the interior of an origin centred circle with arbitrary radius this allows one not only to achieve stability of the filter but also to maintain some safety margins a great advantage of the proposed approach is that it does not impose any constraints on the optimization problem and the optimal filter can be sought using off the shelf optimization procedures the power of the proposed approach is illustrated with filter design examples that compare favorably with results published in research literature

permanents doty coalgebras and dominant dimension of schur algebras abstract a hidden multiplication on a z n r the z dual of the integral schur algebra s z n r is explicitly constructed possibly without a unit the image of the multiplication map is shown to be spanned by bipermanents let k be any field of characteristic p 0 the image of the induced multiplication on a k n r a z n r z k turns out to coincide with the doty coalgebra d n r p of truncated symmetric powers combined with a new straightening formula for bipermanents it is proved that such a multiplication induces an isomorphism a k n r s k n r a k n r a k n r as s k n r bimodules if and only if r n p 1 if and only if d n r p a k n r as a result s k n r is a gendo symmetric algebra and its dominant dimension is at least two and admits a combinatorial characterization as long as r n p 1

stable iir notch filter design with optimal pole placement this paper presents a two stage approach for designing an infinite impulse response iir notch filter first the numerator of the transfer function of the iir notch filter is obtained by placing the zeros at the prescribed notch frequencies then the denominator polynomial is determined by using an iterative scheme in which the optimal pole placements are found by solving a standard quadratic programming problem for stability the pole radius in the single notch filter design is specified by the designer and in the multiple notch filter design the pole radius is constrained by using the implications of rouche s theorem examples are included to illustrate the effectiveness of the proposed techniques

schur functors and schur complexes the study of schur functors has a relatively long history its main impetus derived from representation theory originally in characteristic zero over the years however with the development of modular representations and algebraic geometry over fields of positive characteristic the need for a theory of universal polynomial functors increased and since the mid 1960s approaches to a characteristic free treatment of schur functors have been developing see for instance the recent book of green 1 l in which the treatments by carter and lusztig 6 higman 12 and towber 20 among others are discussed our own interest in such a treatment was awakened by the work of lascoux 141 on resolutions of determinantal ideals although his thesis treated only the characteristic zero case it suggested that a general and elementary theory of schur functors could be developed using only the rudiments of multilinear algebra involving the hopf algebra structures of the symmetric exterior and divided power algebras moreover this elementary development admitted of a natural generalization to the idea of schur complexes whose usefulness was demonstrated for instance in our construction of a universal minimal

a midas approach to modeling first and second moment dynamics abstract we propose a new approach to predictive density modeling that allows for midas effects in both the first and second moments of the outcome specifically our modeling approach allows for midas stochastic volatility dynamics generalizing a large literature focusing on midas effects in the conditional mean and allows the models to be estimated by means of standard gibbs sampling methods when applied to monthly time series on growth in industrial production and inflation we find strong evidence that the introduction of midas effects in the volatility equation leads to improved in sample and out of sample density forecasts our results also suggest that model combination schemes assign high weight to midas in volatility models and produce consistent gains in out of sample predictive performance