closed form solution of local shape from shading at critical points in the theory of shape from shading behaviours of the local solution around a critical point of the image play an important role this paper shows that the second derivatives of the object surface can be locally determined at these image critical points closed form expressions of the surface second derivatives in terms of the second derivatives of the image brightness and of the reflectance map are shown they are derived as follows by differentiating the image irradiance equation twice at an image critical point a set of polynomial equations is obtained that contains the second derivatives of the surface of the image brightness and of the reflectance map regarding these equations as simultaneous equations for unknown surface second derivatives they are algebraically solved and their explicit expressions are derived such a derivation is possible only at image critical points and is impossible at any other image point the applicability of the derived expressions to noisy images is tested using synthetic images

heights of heegner cycles and derivatives of l series 0 introduction 99 1 intersections and heights 103 2 kuga sato varieties and cm cycles 117 3 heights of cm cycles 124 4 heights of heegner cycles 137 5 proof of the main identity and the consequences 147 references 151

a viscosity solutions approach to shape from shading the problem of recovering a lambertian surface from a single two dimensional image may be written as a first order nonlinear equation which presents the disadvantage of having several continuous and even smooth solutions a new approach based on hamilton jacobi bellman equations and viscosity solutions theories enables one to study non uniqueness phenomenon and thus to characterize the surface among the various solutions a consistent and monotone scheme approximating the surface is constructed thanks to the dynamic programming principle and numerical results are presented

duality for ext groups and extensions of discrete series for graded hecke algebras in this paper we study extensions of graded affine hecke algebra modules in particular based on an explicit projective resolution on graded affine hecke algebra modules we prove a duality result for ext groups this duality result with an ind res resolution gives an algebraic proof of the fact that all higher ext groups between a tempered module and a discrete series vanish

the eikonal equation some results applicable to computer vision in this paper we investigate certain first order partial differential equations which formulate the relationship between the light reflected from a surface and its shape particular emphasis is given to eikonal equations two results are presented first we prove that a special type of eikonal equation has only one convex and positive c2 solution in some neighborhood of a singular point using this result we show that a restricted form of this equation has exactly two solutions these results have application in scanning electron microscopy

improved methods of estimating shape from shading using the light source coordinate system abstract this paper develops improved methods of estimating local surface orientation from shading information with the aid of a coordinate system having one axis in the assumed direction of the light source in this system the surface tilt is related to the direction of the gray level gradient at the given point an alternative formulation of the surface slant probability density is developed that takes the discrete nature of digital images into account and that yields a better estimate of the light source direction

regular articlethe structure of the young symmetrizers for spin representations of the symmetric group ii the first paper in this series established that the projective analogue of the young symmetrizer recently introduced by nazarov has a naturalpxq structure comparable with thepq form of the classical symmetrizer this second paper develops the theory on this decomposition further a more efficient construction of the projective symmetrizer is presented for certain classes of partitions this approach yields a compact expression for the intermediate factorx in the projective decomposition

relations between young s natural and the kazhdan lusztig representations of sn abstract our main result here is that under a suitable order of standard tableaux the classical representation of sn introduced by young in the collected papers of alfred young 1873 1940 univ of toronto press toronto qsa iv and usually referred as the natural representattion the the more recently discovered invent math 53 1979 165 184 kazhdan lusztig k l representation are related by an upper triangular integral matrix with unit diagonal elements we have been led to this discovery by a numerical exploration we noted it in each of the irreducible representations of sn up to n 6 the calculations in these cases were carried out by constructing the corresponding kazhdan lusztig graphs from tables m goresky tables of kazhdan lusztig polynomials unpublished of k l polynomials to extend the calculations to n 7 we have used graphs obtained by means of an algorithm given by lascoux and schutzenberger polynomes de kazhdan lusztig pour les grassmanniennes preprint remarkably the same property holds also for these graphs these findings appear to confirm the assertion made by these authors that their algorithm does indeed yield k l graphs for the case of hook shapes we have obtained an explicit construction of the transforming matrices a result which was also suggested by our numerical data for general shapes the transforming matrices are less explicit and our proof is based on certain properties of the kazhdan lusztig representations given in their article invent math 53 1979 165 184 and on a purely combinatorial construction of the natural representation

projective representations of symmetric groups via sergeev duality in this article we determine the irreducible projective representations of the symmetric group sd and the alternating group ad over an algebraically closed field of characteristic p 6 2 these matters are well understood in the case p 0 thanks to the fundamental work of schur 24 in 1911 as well as the much more recent work of nazarov 19 20 sergeev 25 26 and others so the focus here is primarily on the case of positive characteristic where surprisingly little is known as yet in particular we obtain a natural combinatorial labelling of the irreducibles in terms of a certain set rpp d of restricted p strict partitions of d such partitions arose recently in work of kashiwara miwa peterson and yung 11 and leclerc and thibon 14 on the q deformed fock space of the affine kac moody algebra of type a p 1 leclerc and thibon proposed that rpp d should label the irreducible projective representations in some natural way and we show here how this can be done note that for p 3 5 the labelling problem was solved in 1 3 while if p 2 all projective representations of sd and ad are linear so do not need to be considered further here to be more precise recall that is a partition of d if 1 2 is a non increasing sequence of non negative integers summing to d call p strict if in addition

estimates for rankin selberg l functions and quantum unique ergodicity abstract subconvex bounds in the weight aspect for rankin selberg l functions associated to two cusp forms are established these bounds are applied to prove the equidistribution of mass conjecture for cm forms

affine sergeev algebra and q analogues of the young symmetrizers for projective representations of the symmetric group we study a q deformation for the crossed product of the symmetric group s n with the clifford algebra on n anticommuting generators we obtain a q version of the projective analogue for the classical young symmetrizer introduced by the second author our main tool is an analogue of the hecke algebra of complex valued functions on the group mbox gl n over a p adic field relative to the iwahori subgroup

uniqueness in shape from shading for general images of smooth objects wholly contained in the field of view and for illumination symmetric around the viewing direction it is proven that shape is uniquely determined by shading thus shape from shading is a well posed problem under these illumination conditions and regularization is unnecessary for surface reconstruction and should be avoided generic properties of surfaces and images are established questions of existence are also discussed under the conditions above it is argued that most images are effectively impossible with no corresponding physically reasonable surface and that any image can be rendered effectively impossible by a small perturbation of its intensities this is explicitly illustrated for a synthetic image the proofs are based on ideas of dynamical systems theory and global analysis

spin hecke algebras of finite and affine types we introduce the spin hecke algebra which is a q deformation of the spin symmetric group algebra and its affine generalization we establish an algebra isomorphism which relates our spin affine hecke algebras to the affine hecke clifford algebras of olshanski and jones nazarov relation between the spin affine hecke algebra and a nonstandard presentation of the usual affine hecke algebra is displayed and the notion of covering affine hecke algebra is introduced to provide a link between these algebras various algebraic structures for the spin affine hecke algebra are established

spin nilhecke algebras of classical type abstract we formulate and study the spin nilhecke algebras nh n b and nh n d of type b d which differ from the usual nilhecke algebras by some odd signs the type b spin nilhecke algebra is a nil version of the spin type b hecke algebra introduced earlier by the second author and khongsap but not for the type d one we construct faithful polynomial representations pol n of the nilhecke algebras via odd demazure operators we formulate the spin schubert polynomials and use them to show that the spin nilhecke algebras are matrix algebras with entries in a subalgebra of pol n consisting of spin symmetric polynomials all these results have their counterparts for the usual nilhecke algebras over the rational field our work is a generalization of results of lauda and ellis khovanov lauda in usual spin type a

shape from shading level set propagation and viscosity solutions we present a new implementation of an algorithm aimed at recovering a 3d shape from its 2d gray level picture in order to reconstruct the shape of the object an almost arbitrarily initialized 3d function is propagated on a rectangular grid so that a level set of this function tracks the height contours of the shape the method imports techniques from differential geometry fluid dynamics and numerical analysis and provides an accurate shape from shading algorithm the method solves some topological problems and gracefully handles cases of non smooth surfaces that give rise to shocks in the propagating contours real and synthetic images of 3d profiles were submitted to the algorithm and the reconstructed surfaces are presented demonstrating the effectiveness of the proposed method

the projective representations of the hyperoctahedral group the hyperoctahedral group the weyl group of the root system bn has seven distinct nonsplit double covers for n 4 and hence seven families of projective representations we give constructions of all the irreducible representations of these seven double covers in terms of symmetric group representations and determine the associated character tables as a corollary we also obtain the irreducible projective representations and characters of the weyl group of the root system dn

yangian of the queer lie superalgebra consider the complex matrix lie superalgebra with the standard generators where define an involutory automorphism of by the twisted polynomial current lie superalgebra has a natural lie co superalgebra structure we quantise the universal enveloping algebra as a co poisson hopf superalgebra for the quantised algebra we give a description of the centre and construct the double in the sense of drinfeld we also construct a wide class of irreducible representations of the quantised algebra

a categorification of twisted heisenberg algebras abstract we categorify a quantized twisted heisenberg algebra associated to a finite subgroup of sl 2 c

rankin selberg l functions in the level aspect keywords moments rankin selberg convolution level aspect convexity breaking reference tan article 2002 003doi 10 1215 s0012 7094 02 11416 1 record created on 2008 11 14 modified on 2017 05 12

clifford algebra as quantum language we suggest clifford algebra as a useful simplifying language for present quantum dynamics clifford algebras arise from representations of the permutation groups as they arise from representations of the rotation groups aggregates using such representations for their permutations obey clifford statistics the vectors supporting the clifford algebras of permutations and rotations are plexors and spinors respectively physical spinors may actually be plexors describing quantum ensembles not simple individuals we use clifford statistics to define quantum fields on a quantum space time and to formulate a quantum dynamics field space time unity that evades the compactification problem the quantum bits of history regarded as a quantum computation seem to obey a clifford statistics

the structure of the young symmetrizers for spin representations of the symmetric group i abstract this paper is the first in a series of three papers on the young symmetrizers for the spin representations of the symmetric group in this opening paper it is shown that the projective analogue of the young symmetrizer recently introduced by nazarov has a structure resembling thep q form exhibited by the classical symmetrizer in contrast to the classical case our decomposition of the projective symmetrizer requires an additional intermediate factorx this factor will be studied in greater detail in the later papers

cocenters of hecke clifford and spin hecke algebras abstract we determine a basis of the cocenter i e the trace or zeroth hochschild homology of the degenerate affine hecke clifford and spin hecke algebras in classical types

height and gradient from shading the method described here for recovering the shape of a surface from a shaded image can deal with complex wrinkled surfaces integrability can be enforced easily because both surface height and gradient are represented the robustness of the method stems in part from linearization of the reflectance map about the current estimate of the surface orientation at each picture cell the new scheme can find an exact solution of a given shape from shading problem even though a regularizing term is included this is a reflection of the fact that shape from shading problems are it not ill posed when boundary conditions are available or when the image contains singular points

degenerate affine hecke algebras and centralizer construction for the symmetric groups in our recent papers the centralizer construction was applied to the series of classical lie algebras to produce the quantum algebras called twisted yangians here we extend this construction to the series of the symmetric groups s n we study the stable properties of the centralizers of s n m in the group algebra c s n as n with m fixed we construct a limit centralizer algebra a and describe its algebraic structure the algebra a turns out to be closely related with the degenerate affine hecke algebras we also show that the so called tame representations of s yield a class of natural a modules

type a blocks of super category o we show that every block of category oo for the general linear lie superalgebra glm n k glm n k is equivalent to some corresponding block of category oo for the queer lie superalgebra qm n k qm n k this implies the truth of the kazhdan lusztig conjecture for the so called type a blocks of category oo for the queer lie superalgebra as formulated by cheng kwon and wang

parametric shape from shading by radial basis functions we present a new method of shape from shading by using radial basis functions to parameterize the object depth the radial basis functions are deformed by adjusting their centers widths and weights such that the intensity errors are minimized the initial centers and widths are arranged hierarchically to speed up convergence and to stabilize the solution although the smoothness constraint is used it can be eventually dropped out without causing instabilities in the solution an important feature of our parametric shape from shading method is that it offers a unified framework for integration of multiple sensory information we show that knowledge about surface depth and or surface normals anywhere in the image can be easily incorporated into the shape from shading process it is further demonstrated that even qualitative knowledge can be used in shape from shading to improve 3d reconstruction experimental comparisons of our method with several existing ones are made by using both synthetic and real images results show that our solution is more accurate than the others

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

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

hecke clifford algebras and spin hecke algebras iii the trigonometric type abstract the notions of trigonometric spin double affine hecke algebras tsdaha and trigonometric double affine hecke clifford algebras tdahca associated to classical weyl groups are introduced the pbw basis property is established an algebra isomorphism relating tdahca to tsdaha is obtained