Much has been studied about an almost complex structure these ten years. One of the problems about the structure is to find an affine connection which makes a given almost complex tensor field parallel. A Riemannian connection is a one without torsion for which the fundamental tensor field of a Riemannian manifold is parallel. Affine connections on the group manifold were investigated fully by E. Cartan in [1]. In this paper we treat in general some tensor fields and affine connections which make the fields parallel. Moreover some studies about certain tensor fields are given.

In [3], the author studied certain local integrals derived from Fourier coefficient computations on Eisenstein series. Members of a family of Dirichlet series were characterized as a product of an explicit term with a mysterious polynomial factor. In a recent letter to the author, Professor Shoyu Nagaoka asked specific questions concerning the polynomial factor. Several of these questions can be answered by the techniques in [3]. In Part I of that paper, the relevant term is described precisely; however, in Part II, the term is described as a mysterious, albeit finite, sum. The present paper complete [3] by recording what little is known of that sum.

The purpose of this paper is the study of some basic properties of universal induced characters and their applications to the representation theory of the classical groups (for the definition of a universal induced character, see § 3).

The starting point was the paper [F] by E. Formanek on matrix invariants. In his paper [F], Formanek has investigated the Hilbert series for the ring of matrix invariants from the point of view of the representation theory of the general linear group and the symmetric group. In this paper we shall study polynomial concomitants of a group from the same point of view.

We call a second order differential P(z)dxdy on a Riemann surface R a density if it is not identically zero and P(z) is a nonnegative Hölder continuous function of the local parameter z = x + iy in each parametric disk. To each density P on R we associate the linear space P(R) of C2 solutions of the equation Δu(z) = P(z)u(z) invariantly defined on R. We also consider subspaces PX(R) of P(R) consisting of solutions with certain boundedness properties X.

Let p and ℓ be two distinct primes. The aim of this paper is to show how, under a certain congruence hypothesis, the mod ℓ cohomology complex of the Lubin-Tate tower, together with a natural Lefschetz operator, provides a geometric interpretation of Vignéras’s local Langlands correspondence modulo ℓ for unipotent representations.

Let M be a compact C∞ Riemannian manifold, X a Killing vector field on M, and φt its 1-parameter group of isometries of M. In this, paper, we obtain some basic properties of the set of periodic points of φt. We show that the set of least periods is always finite, and the set P(X, t) of points of M having least period t for the vector field X is a totally geodesic submanifold, with possibly non-empty boundary. Moreover, we show there are at least m geometrically distinct closed geodesic orbits of φt, where m is the number of least periods which are not integral multiples of any other least period.

Introduction 1. If denotes the local time of a continuous semi-martingale X at a Bouleau and Yor [1] have obtained a form of Ito’s differentiation formula which states that for absolutely continuous functions F(x)

The main aim of this article is to give sufficient conditions for a family of meromorphic mappings of a domain D in ℂn into ℙN(ℂ) to be meromorphically normal if they satisfy only some very weak conditions with respect to moving hypersurfaces in ℙN(ℂ), namely, that their intersections with these moving hypersurfaces, which moreover may depend on the meromorphic maps, are in some sense uniform. Our results generalize and complete previous results in this area, especially the works of Fujimoto, Tu, Tu-Li, Mai-Thai-Trang, and the recent work of Quang-Tan.

We study a quadruple sequence and express its common limit by Lauricella’s hypergeometric function FD(¼,¼,¼.¼, 1; z1, z2, z3)of three variables. We give a functional equation of FD, which is the key to get our expression of the common limit.

In 2007, Shimoda, in connection with a long-standing question of Sally, asked whether a Noetherian local ring, such that all its prime ideals different from the maximal ideal are complete intersections, has Krull dimension at most 2. In this paper, having reduced the conjecture to the case of dimension 3, if the ring is regular and local of dimension 3, we explicitly describe a family of prime ideals of height 2 minimally generated by three elements. Weakening the hypothesis of regularity, we find that, to achieve the same end, we need to add extra hypotheses, such as completeness, infiniteness of the residue field, and the multiplicity of the ring being at most 3. In the second part of the paper, we turn our attention to the category of standard graded algebras. A geometrical approach via a double use of a Bertini theorem, together with a result of Simis, Ulrich, and Vasconcelos, allows us to obtain a definitive answer in this setting. Finally, by adapting work of Miller on prime Bourbaki ideals in local rings, we detail some more technical results concerning the existence in standard graded algebras of homogeneous prime ideals with an (as it were) excessive number of generators.

Let k be a field and let A = be a normal graded subring of the full ring of polynomials R = k[X1, · · ·, Xn] (where R always is graded via total degree and A0 = k). R. Fossum and the author [F-G] observed that the completion  at the irrelevant maximal ideal of A is isomorphic to the subring of the formal power series ring R̂ = k[[X1, · ·., Xn]] and, moreover, that  is a ring of invariants of an algebraic group whenever A is.

Fundamental calculations on singular invariant hyperfunctions on the n ×n square matrix space and on the 2n × 2n alternating matrix space are considered in this paper. By expanding the complex powers of the determinant function or the Pfaffian function into the Laurent series with respect to the complex parameter, we can construct singular invariant hyperfunctions as their Laurent expansion coefficients. The author presents here the exact orders of the poles of the complex powers and determines the exact supports of the Laurent expansion coefficients. By applying these results, we prove that every quasi-relatively invariant hyperfunction can be expressed as a linear combination of the Laurent expansion coefficients of the complex powers and that every singular quasi-relatively invariant hyperfunction is in fact relatively invariant on the generic points of its support. In the last section, we give the formula of the Fourier transforms of singular invariant tempered distributions.

A conjecture of Bonnafé, Geck, Iancu, and Lam parametrizes Kazhdan-Lusztig left cells for unequal-parameter Hecke algebras in type Bn by families of standard domino tableaux of arbitrary rank. Relying on a family of properties outlined by Lusztig and the recent work of Bonnafé, we verify the conjecture and describe the structure of each cell as a module for the underlying Weyl group.

Let

be a parabolic differential operator defined in Ω = Rn + (0, ∞), where Rn is the n-dimensional Euclidean space, the point x ∈ Rn is represented by its coordinates (x1,...,xn) and aij(=aji), bi and c are functions in (x,t)∈Ω.

Dans toute la suite Xdésignera un groupe abélien localement compact et séparé, et ξdésignera la mesure de Haar sur X.Pour simplifier la discussion, on supposera toujours que Xest à base dénombrable.

Récemment J. L. Doob [8] a trouvé quelques théorèmes intéressants sur l’allure des fonctions méromorphes au voisinage d’un point singulier essentiel isolé en utilisant la topologie fine c’est-à-dire la topologie la moins fine qui fait toutes les fonctions sous-harmoniques continues. A l’égard de ces résultats, on étudie dans ce mémoire quelques aspects de fonctions méromorphes au voisinage d’un point singulier essentiel isolé ou d’un point-frontière irrégulier.

Since J.Wahl ([27]), it is known that degree d plane curves having some fixed numbers of nodes and cusps as its only singularities can be represented by a scheme, let say H, which can be singular. In Wahl’s example, H is singular along a subscheme F but the induced reduced scheme Hred is smooth along F. In this work, we construct explicitly a family of plane curves with nodes and cusps which are represented by singular points of Hred.

To this end, we begin to show that the Hilbert scheme of smooth and connected space curves of degree 12 and genus 15 is irreducible and generically smooth. It follows that it is singular along a hypersurface (3.10). This example is minimal in the sense that the Hilbert scheme of smooth and connected space curves is regular in codimension 1 for d < 12 (B.2). Finally we construct our plane curves from the space curves represented by points of this hypersurface (4.7).

The main subject in the present article has the origin in the following quite primitive question: Linear systems of ordinary differential equations form a nice family. Then, from the projective point of view, what does correspond to linear systems?

We characterize the tight closure of a homogeneous primary ideal in a normal homogeneous coordinate ring over an elliptic curve by a numerical condition and we show that it is in positive characteristic the same as the plus closure.