generic singularities of nilpotent orbit closures according to a theorem of brieskorn and slodowy the intersection of the nilpotent cone of a simple lie algebra with a transverse slice to the subregular nilpotent orbit is a simple surface singularity at the opposite extremity of the poset of nilpotent orbits the closure of the minimal nilpotent orbit is also an isolated symplectic singularity called a minimal singularity for classical lie algebras kraft and procesi showed that these two types of singularities suffice to describe all generic singularities of nilpotent orbit closures specifically any such singularity is either a simple surface singularity a minimal singularity or a union of two simple surface singularities of type a 2k 1 in the present paper we complete the picture by determining the generic singularities of all nilpotent orbit closures in exceptional lie algebras up to normalization in a few cases we summarize the results in some graphs at the end of the paper in most cases we also obtain simple surface singularities or minimal singularities though often with more complicated branching than occurs in the classical types there are however six singularities that do not occur in the classical types three of these are unibranch non normal singularities an sl 2 c variety whose normalization is a 2 an sp 4 c variety whose normalization is a 4 and a two dimensional variety whose normalization is the simple surface singularity a 3 in addition there are three 4 dimensional isolated singularities each appearing once we also study an intrinsic symmetry action on the singularities extending slodowy s work for the singularity of the nilpotent cone at a point in the subregular orbit

normally ordering some multimode exponential operators by virtue of the iwop technique the author shows that the technique of integration within an ordered product iwop provides one with a very simple approach to deriving the normal product form of some multimode exponential operators which greatly simplifies the calculations of normalising some state vectors in hilbert space

unexplained factors and their effects on second pass r squared s we construct the large sample distributions of the ols and gls r2r2 s of the second pass regression of the fama and macbeth 1973 two pass procedure when the observed proxy factors are minorly correlated with the true unobserved factors this implies an unexplained factor structure in the first pass residuals and consequently a large estimation error in the estimated beta s which is spanned by the beta s of the unexplained true factors the average portfolio returns and the estimation error of the estimated beta s are then both linear in the beta s of the unobserved true factors which leads to possibly large values of the ols r2r2 of the second pass regression these large values of the ols r2r2 are not indicative of the strength of the relationship our results question many empirical findings that concern the relationship between expected portfolio returns and macro economic factors

a test of the efficiency of a given portfolio a test for the ex ante efficiency of a given portfolio of assets is analyzed the relevant statistic has a tractable small sample distribution its power function is derived and used to study the sensitivity of the test to the portfolio choice and to the number of assets used to determine the ex post mean variance efficient frontier several intuitive interpretations of the test are provided including a simple mean standard deviation geometric explanation a univariate test equivalent to our multivariate based method is derived and it suggests some useful diagnostic tools which may explain why the null hypothesis is rejected empirical examples suggest that the multivariate approach can lead to more appropriate conclusions than those based on traditional inference which relies on a set of dependent univariate statistics

instrumental variables regression with weak instruments this paper develops asymptotic distribution theory for instrumental variable regression when the partial correlation between the instruments and a single included endogenous variable is weak here modeled as local to zero asymptotic representations are provided for various instrumental variable statistics including the two stage least squares tsls and limited information maximum likelihood liml estimators and their t statistics the asymptotic distributions are found to provide good approximations to sampling distributions with just 20 observations per instrument even in large samples tsls can be badly biased but liml is in many cases approximately median unbiased the theory suggests concrete quantitative guidelines for applied work these guidelines help to interpret angrist and krueger s 1991 estimates of the returns to education whereas tsls estimates with many instruments approach the ols estimate of 6 the more reliable liml and tsls estimates with fewer instruments fall between 8 and 10 with a typical confidence interval of 6 14

arbitrage factor structure and mean variance analysis on large asset markets we examine the implications of arbitrage in a market with many assets the absence of arbitrage opportunities implies that the linear functionals that give the mean and cost of a portfolio are continuous hence there exist unique portfolios that represent these functionals these portfolios span the mean variance efficient set we resolve the question of when a market with many assets permits so much diversification that risk free investment opportunities are available ross 12 14 showed that if there is a factor structure then the mean returns are approximately linear functions of factor loadings we define an approximate factor structure and show that this weaker restriction is sufficient for ross result if the covariance matrix of the asset returns has only k unbounded eigenvalues then there is an approximate factor structure and it is unique the corresponding k eigenvectors converge and play the role of factor loadings hence only a principal component analysis is needed in empirical work

quantum reduction for affine superalgebras we extend the homological method of quantization of generalized drinfeld sokolov reductions to affine superalgebras this leads in particular to a unified representation theory of superconformal algebras

infinite chiral symmetry in four dimensions we describe a new correspondence between four dimensional conformal field theories with extended supersymmetry and two dimensional chiral algebras the meromorphic correlators of the chiral algebra compute correlators in a protected sector of the four dimensional theory infinite chiral symmetry has far reaching consequences for the spectral data correlation functions and central charges of any four dimensional theory with mathcal n 2 superconformal symmetry

a remark on the c 2 cofiniteness condition on vertex algebras we show that a finitely strongly generated non negatively graded vertex algebra is c 2 cofinite if and only if it is lisse in the sense of beilinson et al preprint this shows that the c 2 cofiniteness is indeed a natural finiteness condition

tests of risk premia in linear factor models abstract we show that statistical inference on the risk premia in linear factor models that is based on the fama macbeth fm and generalized least squares gls two pass risk premia estimators is misleading when the s are small and or the number of assets is large we propose novel statistics that are based on the maximum likelihood estimator of gibbons gibbons m 1982 multivariate tests of financial models a new approach journal of financial economics 10 3 27 which remain trustworthy in these cases the inadequacy of the fm and gls two pass t wald statistics is highlighted in a power and size comparison using quarterly portfolio returns from lettau and ludvigson lettau m ludvigson s 2001 resurrecting the c capm a cross sectional test when risk premia are time varying journal of political economy 109 1238 1287 the power and size comparison shows that the fm and gls two pass t wald statistics can be severely size distorted the 95 confidence sets for the risk premia in the above cited work that result from the novel statistics differ substantially from those that result from the fm and gls two pass t statistics they show support for the human capital asset pricing model although the 95 confidence set for the risk premia on labor income growth is unbounded the 95 confidence sets show no support for the scaled consumption asset pricing model since the 95 confidence set of the risk premia on the scaled consumption growth consists of the whole real line but do not reject it either

spurious inference in reduced rank asset pricing models this note studies some seemingly anomalous results that arise in possibly misspecified reduced rank linear asset pricing models estimated by the continuously updated generalized method of moments when a spurious factor that is a factor that is uncorrelated with the returns on the test assets is present the test for correct model specification has asymptotic power that is equal to the nominal size in other words applied researchers will erroneously conclude that the model is correctly specified even when the degree of misspecification is arbitrarily large the rejection probability of the test for overidentifying restrictions typically decreases further in underidentified models where the dimension of the null space is larger than 1

normality of nilpotent varieties in e6 abstract we determine which nilpotent orbits in e6 have closures which are normal varieties and which do not at the same time we are able to verify a conjecture in e sommers comm math univ sancti pauli 49 1 2000 101 104 concerning functions on non special nilpotent orbits for e6

on the irreducibility of associated varieties of w algebras abstract we investigate the irreducibility of the nilpotent slodowy slices that appear as the associated variety of w algebras furthermore we provide new examples of vertex algebras whose associated variety has finitely many symplectic leaves

asymptotics of the principal components estimator of large factor models with weakly influential factors abstract this paper introduces a drifting parameter asymptotic framework to derive accurate approximations to the finite sample distribution of the principal components pc estimator in situations when the factors explanatory power does not strongly dominate the explanatory power of the cross sectionally and temporally correlated idiosyncratic terms under our asymptotics the pc estimator is inconsistent we find explicit formulae for the amount of the inconsistency and propose an estimator of the number of factors for which the pc estimator works reasonably well for the special case when the idiosyncratic terms are cross sectionally but not temporally correlated or vice versa we show that the coefficients in the ols regressions of the pc estimates of factors loadings on the true factors true loadings are asymptotically normal and find explicit formulae for the corresponding asymptotic covariance matrix we explain how to estimate the parameters of the derived asymptotic distributions our monte carlo analysis suggests that our asymptotic formulae and estimators work well even for relatively small n and t we apply our theoretical results to test a hypothesis about the factor content of the us stock return data

inferential theory for factor models of large dimensions this paper develops an inferential theory for factor models of large dimensions the principal components estimator is considered because it is easy to compute and is asymptotically equivalent to the maximum likelihood estimator if normality is assumed we derive the rate of convergence and the limiting distributions of the estimated factors factor loadings and common components the theory is developed within the framework of large cross sections n and a large time dimension t to which classical factor analysis does not apply we show that the estimated common components are asymptotically normal with a convergence rate equal to the minimum of the square roots of n and t the estimated factors and their loadings are generally normal although not always so the convergence rate of the estimated factors and factor loadings can be faster than that of the estimated common components these results are obtained under general conditions that allow for correlations and heteroskedasticities in both dimensions stronger results are obtained when the idiosyncratic errors are serially uncorrelated and homoskedastic a necessary and sufficient condition for consistency is derived for large n but fixed t

an observation of quadratic algebra dual family of nonlinear coherent states and their non classical properties in the generalized isotonic oscillator in this paper we construct nonlinear coherent states for the generalized isotonic oscillator and study their non classical properties in detail by transforming the deformed ladder operators suitably which generate the quadratic algebra we obtain heisenberg algebra from the algebra we define two non unitary and one unitary displacement type operators while the action of one of the non unitary type operators reproduces the original nonlinear coherent states the other one fails to produce a new set of nonlinear coherent states dual pair we show that these dual states are not normalizable for the nonlinear coherent states we evaluate the parameter a3 and examine the non classical nature of the states through quadratic and amplitude squared squeezing effect further we derive analytical formula for the p function q function and the wigner function for the nonlinear coherent states all of them confirm the non classicality of the nonlinear coherent states in addition to the above we obtain the

statistical properties of a generalized photon modulated thermal state in this paper we introduce a new kind of quantum state generalized photon modulated thermal states gpmts which are obtained by repeatedly acting the superposed operation a coherent superposition of photon subtraction and addition on the thermal state it is found that the normalization factor of gpmts is a legendre polynomial moreover we present the analytical expressions of several quasi probability distributions for gpmts and calculate the corresponding tomogram and photocount distribution as well