bluuebunny/crossref_metadata_2025 huggingface dataset:
Parabolic Subgroups with Abelian Unipotent Radical as a Testing Site for Invariant Theory
Authors: Panyushev Dmitri I.
Published: December 2010

Let L be a simple algebraic group and P a parabolic subgroup with Abelian unipotent radical Pu. Many familiar varieties (determinantal varieties, their symmetric and skew-symmetric analogues) arise as closures of P-orbits in Pu. We give a unified invariant-theoretic treatment of various properties of these orbit closures. We also describe the closures of the conormal bundles of these orbits as the irreducible components of some commuting variety and show that the polynomial algebra k[Pu] is a free module over the algebra of covariants.
Induced Coactions of Discrete Groups on C*-Algebras
Authors: Echterhoff Siegfried , Quigg John
Published: December 2010

Using the close relationship between coactions of discrete groups and Fell bundles, we introduce a procedure for inducing a C*-coaction δ: D → D ⊗C*(G/N) of a quotient group G/N of a discrete group G to a C*-coaction Ind δ: Ind D → D ⊗C*(G) of G. We show that induced coactions behave in many respects similarly to induced actions. In particular, as an analogue of the well known imprimitivity theorem for induced actions we prove that the crossed products Ind D ×IndδG and D ×δG/N are always Morita equivalent. We also obtain nonabelian analogues of a theorem of Olesen and Pedersen which show that there is a duality between induced coactions and twisted actions in the sense of Green. We further investigate amenability of Fell bundles corresponding to induced coactions.
Counting in Ergodic Theory
Authors: Jones Roger L. , Rosenblatt Joseph M. , Wierdl Máté
Published: December 2010

Many aspects of the behavior of averages in ergodic theory are a matter of counting the number of times a particular event occurs. This theme is pursued in this article where we consider large deviations, square functions, jump inequalities and related topics.
The Hausdorff and Packing Dimensions of Some Sets Related to Sierpiński Carpets
Authors: Nielsen Ole A.
Published: December 2010

The Sierpiński carpets first considered by C.McMullen and later studied by Y. Peres are modified by insisting that the allowed digits in the expansions occur with prescribed frequencies. This paper (i) calculates theHausdorff, box (or Minkowski), and packing dimensions of themodified Sierpiński carpets and (ii) shows that for these sets the Hausdorff and packing measures in their dimension are never zero and gives necessary and sufficient conditions for these measures to be infinite.
The Characteristic Numbers of Quartic Plane Curves
Authors: Vakil Ravi
Published: December 2010

The characteristic numbers of smooth plane quartics are computed using intersection theory on a component of the moduli space of stable maps. This completes the verification of Zeuthen’s prediction of characteristic numbers of smooth plane curves. A short sketch of a computation of the characteristic numbers of plane cubics is also given as an illustration.
Corrigendum to “Spectral Theory for the Neumann Laplacian on Planar Domains with Horn-Like Ends”
Authors: Edward Julian
Published: December 2010

Errors to a previous paper (Canad. J. Math. (2) 49(1997), 232–262) are corrected. A non-standard regularisation of the auxiliary operator A appearing in Mourre theory is used.
Sublinearity and Other Spectral Conditions on a Semigroup
Authors: Radjavi Heydar
Published: December 2010

Subadditivity, sublinearity, submultiplicativity, and other conditions are considered for spectra of pairs of operators on a Hilbert space. Sublinearity, for example, is a weakening of the well-known property L and means σ(A + λB) ⊆ σ(A) + λσ(B) for all scalars λ. The effect of these conditions is examined on commutativity, reducibility, and triangularizability of multiplicative semigroups of operators. A sample result is that sublinearity of spectra implies simultaneous triangularizability for a semigroup of compact operators.
Characters of Depth-Zero, Supercuspidal Representations of the Rank-2 Symplectic Group
Authors: Cunningham Clifton
Published: December 2010

This paper expresses the character of certain depth-zero supercuspidal representations of the rank-2 symplectic group as the Fourier transform of a finite linear combination of regular elliptic orbital integrals—an expression which is ideally suited for the study of the stability of those characters. Building on work of F. Murnaghan, our proof involves Lusztig’s Generalised Springer Correspondence in a fundamental way, and also makes use of some results on elliptic orbital integrals proved elsewhere by the author using Moy-Prasad filtrations of p-adic Lie algebras. Two applications of the main result are considered toward the end of the paper.
Multiple Mixing and Rank One Group Actions
Authors: del Junco Andrés , Yassawi Reem
Published: December 2010

Suppose G is a countable, Abelian group with an element of infinite order and let be amixing rank one action of G on a probability space. Suppose further that the Følner sequence {Fn} indexing the towers of satisfies a “bounded intersection property”: there is a constant p such that each {Fn} can intersect no more than p disjoint translates of {Fn}. Then is mixing of all orders. When G = Z, this extends the results of Kalikow and Ryzhikov to a large class of “funny” rank one transformations. We follow Ryzhikov’s joining technique in our proof: the main theorem follows from showing that any pairwise independent joining of k copies of is necessarily product measure. This method generalizes Ryzhikov’s technique.
Geometric and Potential Theoretic Results on Lie Groups
Authors: Varopoulos N. Th.
Published: December 2010

The main new results in this paper are contained in the geometric Theorems 1 and 2 of Section 0.1 below and they are related to previous results of M. Gromov and of myself (cf. [11], [29]). These results are used to prove some general potential theoretic estimates on Lie groups (cf. Section 0.3) that are related to my previous work in the area (cf. [28], [34]) and to some deep recent work of G. Alexopoulos (cf. [3], [4]).
The Level 2 and 3 Modular Invariants for the Orthogonal Algebras
Authors: Gannon Terry
Published: December 2010

The ‘1-loop partition function’ of a rational conformal field theory is a sesquilinear combination of characters, invariant under a natural action of SL2(), and obeying an integrality condition. Classifying these is a clearly defined mathematical problem, and at least for the affine Kac-Moody algebras tends to have interesting solutions. This paper finds for each affine algebraBr(1)andDr(1)all of these at levelk≤ 3. Previously, only those at level 1 were classified. An extraordinary number of exceptionals appear at level 2—theBr(1),Dr(1)level 2 classification is easily the most anomalous one known and this uniqueness is the primary motivation for this paper. The only level 3 exceptionals occur forB2(1)≅C2(1)andD7(1). TheB2,3andD7,3exceptionals are cousins of the ε6-exceptional and ε8-exceptional, respectively, in the A-D-E classification forA1(1), while the level 2 exceptionals are related to the lattice invariants of affineu(1).
On Square-Integrable Representations of Classical p-adic Groups
Authors: Jantzen Chris
Published: December 2010

In this paper, we use Jacquet module methods to study the problem of classifying discrete series for the classical p-adic groups Sp(2n, F) and SO(2n + 1, F).
Symplectic Geometry of the Moduli Space of Flat Connections on a Riemann Surface: Inductive Decompositions and Vanishing Theorems
Authors: Jeffrey Lisa C. , Weitsman Jonathan
Published: December 2010

This paper treats the moduli spaceg,1(Λ) of representations of the fundamental group of a Riemann surface of genusgwith one boundary component which send the loop around the boundary to an element conjugate to exp Λ, where Λ is in the fundamental alcove of a Lie algebra. We construct natural line bundles overg,1(Λ) and exhibit natural homology cycles representing the Poincaré dual of the first Chern class. We use these cycles to prove differential equations satisfied by the symplectic volumes of these spaces. Finally we give a bound on the degree of a nonvanishing element of a particular subring of the cohomology of the moduli space of stable bundles of coprime rankkand degreed.
A Continuous Field of Projectionless C*-Algebras
Authors: Dean Andrew
Published: December 2010

We use some results about stable relations to show that some of the simple, stable, projectionless crossed products of O2 by considered by Kishimoto and Kumjian are inductive limits of type C*-algebras. The type I C*-algebras that arise are pullbacks of finite direct sums of matrix algebras over the continuous functions on the unit interval by finite dimensional C*-algebras.
A Truncated Integral of the Poisson Summation Formula
Authors: Levy Jason
Published: December 2010

Let G be a reductive algebraic group defined over , with anisotropic centre. Given a rational action of G on a finite-dimensional vector space V, we analyze the truncated integral of the theta series corresponding to a Schwartz-Bruhat function on V(). The Poisson summation formula then yields an identity of distributions on V(). The truncation used is due to Arthur.
Classification of Simple Tracially AF C*-Algebras
Authors: Lin Huaxin
Published: December 2010

We prove that pre-classifiable (see 3.1) simple nuclear tracially AF C*-algebras (TAF) are classified by their K-theory. As a consequence all simple, locally AH and TAF C*-algebras are in fact AH algebras (it is known that there are locally AH algebras that are not AH). We also prove the following Rationalization Theorem. Let A and B be two unital separable nuclear simple TAF C*- algebras with unique normalized traces satisfying the Universal Coefficient Theorem. If A and B have the same (ordered and scaled) K-theory and K0(A)+ is locally finitely generated, then A ⊗ Q ≅ B ⊗ Q, where Q is the UHF-algebra with the rational K0. Classification results (with restriction on K0 - theory) for the above C*-algebras are also obtained. For example, we show that, if A and B are unital nuclear separable simple TAF C*-algebras with the unique normalized trace satisfying the UCT and with K1(A) = K1(B), and A and B have the same rational (scaled ordered) K0, then A ≅ B. Similar results are also obtained for some cases in which K0 is non-divisible such as K0(A) = Z[1/2].
Tensor Product Realizations of Simple Torsion Free Modules
Authors: Britten D. J. , Lemire F. W.
Published: December 2010

Let be a finite dimensional simple Lie algebra over the complex numbers C. Fernando reduced the classification of infinite dimensional simple -modules with a finite dimensional weight space to determining the simple torsion free -modules for of type A or C. Thesemodules were determined by Mathieu and using his work we provide a more elementary construction realizing each one as a submodule of an easily constructed tensor product module.
Darboux Transformations for the KP Hierarchy in the Segal-Wilson Setting
Authors: Helminck G. F. , van de Leur J. W.
Published: December 2010

In this paper it is shown that inclusions inside the Segal-Wilson Grassmannian give rise to Darboux transformations between the solutions of the KP hierarchy corresponding to these planes. We present a closed form of the operators that procure the transformation and express them in the related geometric data. Further the associated transformation on the level of τ-functions is given.
Isometric Dilations of Non-Commuting Finite Rank n-Tuples
Authors: Davidson Kenneth R. , Kribs David W. , Shpigel Miron E.
Published: December 2010

A contractive n-tuple A = (A1,…,An) has a minimal joint isometric dilation S = (S1,…,Sn) where the Si’s are isometries with pairwise orthogonal ranges. This determines a representation of the Cuntz-Toeplitz algebra. When A acts on a finite dimensional space, the wot-closed nonself-adjoint algebra generated by S is completely described in terms of the properties of A. This provides complete unitary invariants for the corresponding representations. In addition, we show that the algebra is always hyper-reflexive. In the last section, we describe similarity invariants. In particular, an n-tuple B of d × d matrices is similar to an irreducible n-tuple A if and only if a certain finite set of polynomials vanish on B.
Multi-Sided Braid Type Subfactors
Authors: Erlijman Juliana
Published: December 2010

We generalise the two-sided construction of examples of pairs of subfactors of the hyperfinite II1factorRin [E1]—which arise by considering unitary braid representations with certain properties—to multisided pairs. We show that the index for the multi-sided pair can be expressed as a power of that for the two-sided pair. This construction can be applied to the natural examples—where the braid representations are obtained in connection with the representation theory of Lie algebras of typesA,B,C,D. We also compute the (first) relative commutants.
On Some Exponential Equations of S. S. Pillai
Authors: Bennett Michael A.
Published: December 2010

In this paper, we establish a number of theorems on the classic Diophantine equation of S. S. Pillai, ax – by = c, where a, b and c are given nonzero integers with a, b ≥ 2. In particular, we obtain the sharp result that there are at most two solutions in positive integers x and y and deduce a variety of explicit conditions under which there exists at most a single such solution. These improve or generalize prior work of Le, Leveque, Pillai, Scott and Terai. The main tools used include lower bounds for linear forms in the logarithms of (two) algebraic numbers and various elementary arguments.
Représentations irréductibles bornées des groupes de Lie exponentiels
Authors: Ludwig J. , Molitor-Braun C.
Published: December 2010

Let G be a solvable exponential Lie group. We characterize all the continuous topologically irreducible bounded representations (T, ) of G on a Banach space by giving a G-orbit in n* (n being the nilradical of g), a topologically irreducible representation of L1(ℝn, ω), for a certain weight ω and a certain n ∈ ℕ, and a topologically simple extension norm. If G is not symmetric, i.e., if the weight ω is exponential, we get a new type of representations which are fundamentally different from the induced representations.
The Complete (Lp, Lp) Mapping Properties of Some Oscillatory Integrals in Several Dimensions
Authors: Sampson G. , Szeptycki P.
Published: December 2010

We prove that the operators map Lp(ℝ2) into itself for p ∈ J = if al , bl ≥ 1 and φ(x, y) = |x – y|–r, 0 ≤ r < 2, the result is sharp. Generalizations to dimensions d > 2 are indicated.
Monotone Paths on Zonotopes and Oriented Matroids
Authors: Athanasiadis Christos A. , Santos Francisco
Published: December 2010

Monotone paths on zonotopes and the natural generalization to maximal chains in the poset of topes of an oriented matroid or arrangement of pseudo-hyperplanes are studied with respect to a kind of local move, called polygon move or flip. It is proved that any monotone path on a $d$-dimensional zonotope with $n$ generators admits at least $\left\lceil 2n/\left( n-d+2 \right) \right\rceil -1$ flips for all $n\ge d+2\ge 4$ and that for any fixed value of $n-d$, this lower bound is sharp for infinitely many values of $n$. In particular, monotone paths on zonotopes which admit only three flips are constructed in each dimension $d\ge 3$. Furthermore, the previously known 2-connectivity of the graph of monotone paths on a polytope is extended to the 2-connectivity of the graph of maximal chains of topes of an oriented matroid. An application in the context of Coxeter groups of a result known to be valid for monotone paths on simple zonotopes is included.
On the Milnor Fiber of a Quasi-ordinary Surface Singularity
Authors: Ban Chunsheng , McEwan Lee J. , Némethi András
Published: December 2010

We verify a generalization of (3.3) from [Lê73] proving that the homotopy type of the Milnor fiber of a reduced hypersurface singularity depends only on the embedded topological type of the singularity. In particular, using [Zariski68, Lipman83, Oh93, Gau88] for irreducible quasi-ordinary germs, it depends only on the normalized distinguished pairs of the singularity. The main result of the paper provides an explicit formula for the Euler-characteristic of the Milnor fiber in the surface case.
Convergence Factors and Compactness in Weighted Convolution Algebras
Authors: Ghahramani Fereidoun , Grabiner Sandy
Published: December 2010

We study convergence in weighted convolution algebras L1(ω) on R+, with the weights chosen such that the corresponding weighted space M(ω) of measures is also a Banach algebra and is the dual space of a natural related space of continuous functions. We determine convergence factor ɳ for which weak*-convergence of {λn} to λ in M(ω) implies norm convergence of λn * f to λ * f in L1(ωɳ). We find necessary and sufficent conditions which depend on ω and f and also find necessary and sufficent conditions for ɳ to be a convergence factor for all L1(ω) and all f in L1(ω). We also give some applications to the structure of weighted convolution algebras. As a preliminary result we observe that ɳ is a convergence factor for ω and f if and only if convolution by f is a compact operator from M(ω) (or L1(ω)) to L1(ωɳ).
Equivariant Embeddings into Smooth Toric Varieties
Authors: Hausen Jürgen
Published: December 2010

We characterize embeddability of algebraic varieties into smooth toric varieties and prevarieties. Our embedding results hold also in an equivariant context and thus generalize a well-known embedding theorem of Sumihiro on quasiprojectiveG-varieties. The main idea is to reduce the embedding problem to the affine case. This is done by constructing equivariant affine conoids, a tool which extends the concept of an equivariant affine cone over a projectiveG-variety to a more general framework.
Frames and Single Wavelets for Unitary Groups
Authors: Weber Eric
Published: December 2010

We consider a unitary representation of a discrete countable abelian group on a separable Hilbert space which is associated to a cyclic generalized frame multiresolution analysis. We extend Robertson’s theorem to apply to frames generated by the action of the group. Within this setup we use Stone’s theorem and the theory of projection valued measures to analyze wandering frame collections. This yields a functional analytic method of constructing a wavelet from a generalized frame multiresolution analysis in terms of the frame scaling vectors. We then explicitly apply our results to the action of the integers given by translations on L2(ℝ).
The Valuative Theory of Foliations
Authors: Fortuny Ayuso Pedro
Published: December 2010

This paper gives a characterization of valuations that follow the singular infinitely near points of plane vector fields, using the notion of L'Hôpital valuation, which generalizes a well known classical condition. With that tool, we give a valuative description of vector fields with infinite solutions, singularities with rational quotient of eigenvalues in its linear part, and polynomial vector fields with transcendental solutions, among other results.
Combinatorics of the Heat Trace on Spheres
Authors: Polterovich Iosif
Published: December 2010

We present a concise explicit expression for the heat trace coefficients of spheres. Our formulas yield certain combinatorial identities which are proved following ideas of D. Zeilberger. In particular, these identities allow to recover in a surprising way some known formulas for the heat trace asymptotics. Our approach is based on a method for computation of heat invariants developed in [P].
Multipliers on Vector Valued Bergman Spaces
Authors: Blasco Oscar , Arregui José Luis
Published: December 2010

Let X be a complex Banach space and let Bp(X) denote the vector-valued Bergman space on the unit disc for 1 ≤ p < ∞. A sequence (Tn)n of bounded operators between two Banach spaces X and Y defines a multiplier between Bp(X) and Bq(Y) (resp. Bp(X) and lq(Y)) if for any function we have that belongs to Bq(Y) (resp. (Tn(xn))n ∈ lq(Y)). Several results on these multipliers are obtained, some of them depending upon the Fourier or Rademacher type of the spaces X and Y. New properties defined by the vector-valued version of certain inequalities for Taylor coefficients of functions in Bp(X) are introduced.
Zariski Hyperplane Section Theorem for Grassmannian Varieties
Authors: Shimada Ichiro
Published: December 2010

Let ϕ: X → M be a morphism from a smooth irreducible complex quasi-projective variety X to a Grassmannian variety M such that the image is of dimension ≥ 2. Let D be a reduced hypersurface in M, and γ a general linear automorphism of M. We show that, under a certain differentialgeometric condition on ϕ(X) and D, the fundamental group π1((γ ○ ϕ)−1 (M \ D)) is isomorphic to a central extension of π1(M \ D) × π1(X) by the cokernel of π2(ϕ) : π2(X) → π2(M).
A Generalized Torelli Theorem
Authors: Dhillon Ajneet
Published: December 2010

Given a smooth projective curve C of positive genus g, Torelli's theorem asserts that the pair (J(C), Wg−1) determines C. We show that the theorem is true with Wg−1 replaced by Wd for each d in the range 1 ≤ d ≤ g − 1.
Weak Explicit Matching for Level Zero Discrete Series of Unit Groups of 𝔭-Adic Simple Algebras
Authors: Silberger Allan J. , Zink Ernst-Wilhelm
Published: December 2010

Let F be a p-adic local field and let be the unit group of a central simple F-algebra Ai of reduced degree n > 1 (i = 1, 2). Let ℛ2() denote the set of irreducible discrete series representations of . The “Abstract Matching Theorem” asserts the existence of a bijection, the “Jacquet- Langlands” map, which, up to known sign, preserves character values for regular elliptic elements. This paper addresses the question of explicitly describing the map 𝒥ℒ, but only for “level zero” representations. We prove that the restriction is a bijection of level zero discrete series (Proposition 3.2) and we give a parameterization of the set of unramified twist classes of level zero discrete series which does not depend upon the algebra Ai and is invariant under 𝒥ℒA2,A1 (Theorem 4.1).
Quasi-Homogeneous Linear Systems on ℙ2with Base Points of Multiplicity 5
Authors: Laface Antonio , Ugaglia Luca
Published: December 2010

In this paper we consider linear systems of ℙ2with all but one of the base points of multiplicity 5. We give an explicit way to evaluate the dimensions of such systems.
Automorphic Orthogonal and Extremal Polynomials
Authors: Lukashov A. L. , Peherstorfer F.
Published: December 2010

It is well known that many polynomials which solve extremal problems on a single interval as the Chebyshev or the Bernstein-Szegö polynomials can be represented by trigonometric functions and their inverses. On two intervals one has elliptic instead of trigonometric functions. In this paper we show that the counterparts of the Chebyshev and Bernstein-Szegö polynomials for several intervals can be represented with the help of automorphic functions, so-called Schottky-Burnside functions. Based on this representation and using the Schottky-Burnside automorphic functions as a tool several extremal properties of such polynomials as orthogonality properties, extremal properties with respect to the maximum norm, behaviour of zeros and recurrence coefficients etc. are derived.
Quaternions and Some Global Properties of Hyperbolic 5-Manifolds
Authors: Kellerhals Ruth
Published: December 2010

We provide an explicit thick and thin decomposition for oriented hyperbolic manifolds M of dimension 5. The result implies improved universal lower bounds for the volume vol5(M) and, for M compact, new estimates relating the injectivity radius and the diameter of M with vol5(M). The quantification of the thin part is based upon the identification of the isometry group of the universal space by the matrix group PSΔ L(2, ℍ) of quaternionic 2 × 2-matrices with Dieudonné determinant Δ equal to 1 and isolation properties of PSΔ L(2, ℍ).
Selmer Groups of Elliptic Curves with Complex Multiplication
Authors: Saikia A.
Published: December 2010

Suppose K is an imaginary quadratic field and E is an elliptic curve over a number field F with complex multiplication by the ring of integers in K. Let p be a rational prime that splits as in K. Let Epn denote the pn-division points on E. Assume that F(Epn) is abelian over K for all n ≥ 0. This paper proves that the Pontrjagin dual of the -Selmer group of E over F(Ep∞) is a finitely generated free Λ-module, where Λ is the Iwasawa algebra of . It also gives a simple formula for the rank of the Pontrjagin dual as a Λ-module.
Asymptotics for Minimal Discrete Riesz Energy on Curves in ℝd
Authors: Martínez-Finkelshtein A. , Maymeskul V. , Rakhmanov E. A. , Saff E. B.
Published: December 2010

We consider the s-energy for point sets 𝒵 = {𝒵k,n: k = 0, …, n} on certain compact sets Γ in ℝd having finite one-dimensional Hausdorff measure,

is the Riesz kernel. Asymptotics for the minimum s-energy and the distribution of minimizing sequences of points is studied. In particular, we prove that, for s ≥ 1, the minimizing nodes for a rectifiable Jordan curve Γ distribute asymptotically uniformly with respect to arclength as n → ∞.
Solvable Points on Projective Algebraic Curves
Authors: Pál Ambrus
Published: December 2010

We examine the problem of finding rational points defined over solvable extensions on algebraic curves defined over general fields. We construct non-singular, geometrically irreducible projective curves without solvable points of genus g, when g is at least 40, over fields of arbitrary characteristic. We prove that every smooth, geometrically irreducible projective curve of genus 0, 2, 3 or 4 defined over any field has a solvable point. Finally we prove that every genus 1 curve defined over a local field of characteristic zero with residue field of characteristic p has a divisor of degree prime to 6p defined over a solvable extension.
Lie Elements and Knuth Relations
Authors: Schocker Manfred
Published: December 2010

A coplactic class in the symmetric groupconsists of all permutations inwith a given SchenstedQ-symbol, and may be described in terms of local relations introduced by Knuth. Any Lie element in the group algebra ofwhich is constant on coplactic classes is already constant on descent classes. As a consequence, the intersection of the Lie convolution algebra introduced by Patras and Reutenauer and the coplactic algebra introduced by Poirier and Reutenauer is the direct sum of all Solomon descent algebras.
K-Homology of the Rotation Algebras Aθ
Authors: Hadfield Tom
Published: December 2010

We study the K-homology of the rotation algebras Aθ using the six-term cyclic sequence for the K-homology of a crossed product by Z. In the case that θ is irrational, we use Pimsner and Voiculescu's work on AF-embeddings of the Aθ to search for the missing generator of the even K-homology.
Division par un polynôme hyperbolique
Authors: Chaumatet Jacques , Chollet Anne-Marie
Published: December 2010

On se donne un intervalle ouvert non vide ω de ℝ, un ouvert connexe non vide Ω de ℝset unpolynôme unitaire

de degrém> 0, dépendant du paramètre λ ∈ Ω. Un tel polynôme est dit ω-hyperbolique si, pour tout λ ∈ Ω, ses racines sont réelles et appartiennent à ω.

On suppose que les fonctionsak,k= 1, … ,m, appartiennent à une classe ultradifférentiableCM(Ω). On s‘intéresse au problème suivant. Soitfappartient àCM(Ω), existe-t-il des fonctionsQfetRf, k,k= 0, … ,m–1, appartenant respectivement àCM(ω × Ω) et àCM(Ω), telles que l’on ait, pour (x, λ) ∈ ω × Ω,

On donne ici une réponse positive dès que le polynôme est ω-hyperbolique, que la class untradifférentiable soit quasi-analytique ou non ; on obtient alors, des exemples d’idéaux fermés dansCM(ℝn). On complète ce travail par une généralisation d’un résultat de C. L. Childress dans le cadre quasi-analytique et quelques remarques.
Meromorphic Functions Sharing the Same Zeros and Poles
Authors: Frank Günter , Hua Xinhou , Vaillancourt Rémi
Published: December 2010

In this paper, Hinkkanen's problem (1984) is completely solved, i.e., it is shown that any meromorphic function f is determined by its zeros and poles and the zeros of f(j) for j = 1, 2, 3, 4.
Bending Flows for Sums of Rank One Matrices
Authors: Flaschka Hermann , Millson John
Published: December 2010

We study certain symplectic quotients ofn-fold products of complex projectivem-space by the unitary group acting diagonally. After studying nonemptiness and smoothness of these quotients we construct the action-angle variables, defined on an open dense subset, of an integrable Hamiltonian system. The semiclassical quantization of this system reporduces formulas from the representation theory of the unitary group.
Duality and Supports of Induced Representations for Orthogonal Groups
Authors: Jantzen Chris
Published: December 2010

In this paper, we construct a duality for p-adic orthogonal groups.
Certain Exponential Sums and Random Walks on Elliptic Curves
Authors: Lange Tanja , Shparlinski Igor E.
Published: December 2010

For a given elliptic curve E, we obtain an upper bound on the discrepancy of sets of multiples zsG where zs runs through a sequence Z = (z1, … , zT) such that kz1, … , kzT is a permutation of z1, … , zT, both sequences taken modulo t, for sufficiently many distinct values of k modulo t.

We apply this result to studying an analogue of the power generator over an elliptic curve. These results are elliptic curve analogues of those obtained for multiplicative groups of finite fields and residue rings.
Approximating Flats by Periodic Flats in CAT(0) Square Complexes
Authors: Wise Daniel T.
Published: December 2010

We investigate the problem of whether every immersed flat plane in a nonpositively curved square complex is the limit of periodic flat planes. Using a branched cover, we reduce the problem to the case of VH-complexes. We solve the problem for malnormal and cyclonormal VH-complexes. We also solve the problem for complete square complexes using a different approach. We give an application towards deciding whether the elements of fundamental groups of the spaces we study have commuting powers. We note a connection between the flat approximation problem and subgroup separability.
Some Results on Surfaces of General Type
Authors: Purnaprajna B. P.
Published: December 2010

In this article we prove some new results on projective normality, normal presentation and higher syzygies for surfaces of general type, not necessarily smooth, embedded by adjoint linear series. Some of the corollaries of more general results include: results on property Np associated to KS ⊗B⊗n where B is base-point free and ample divisor with B⊗K* nef, results for pluricanonical linear systems and results giving effective bounds for adjoint linear series associated to ample bundles. Examples in the last section show that the results are optimal.
Sur la structure transverse à une orbite nilpotente adjointe
Authors: Sabourin Hervé
Published: December 2010

We are interested in Poisson structures transverse to nilpotent adjoint orbits in a complex semi-simple Lie algebra, and we study their polynomial nature. Furthermore, in the case of sln, we construct some families of nilpotent orbits with quadratic transverse structures.
On the Vanishing of μ-Invariants of Elliptic Curves over ℚ
Authors: Trifković Mak
Published: December 2010

Let E/ℚ be an elliptic curve with good ordinary reduction at a prime p > 2. It has a welldefined Iwasawa μ-invariant μ(E)p which encodes part of the information about the growth of the Selmer group ) as Kn ranges over the subfields of the cyclotomic Zp-extension K∞/ℚ. Ralph Greenberg has conjectured that any such E is isogenous to a curve E′ with μ(E′)p = 0. In this paper we prove Greenberg's conjecture for infinitely many curves E with a rational p-torsion point, p = 3 or 5, no two of our examples having isomorphic p-torsion. The core of our strategy is a partial explicit evaluation of the global duality pairing for finite flat group schemes over rings of integers.
Petrie Schemes
Authors: Williams Gordon
Published: December 2010

Petrie polygons, especially as they arise in the study of regular polytopes and Coxeter groups, have been studied by geometers and group theorists since the early part of the twentieth century. An open question is the determination of which polyhedra possess Petrie polygons that are simple closed curves. The current work explores combinatorial structures in abstract polytopes, called Petrie schemes, that generalize the notion of a Petrie polygon. It is established that all of the regular convex polytopes and honeycombs in Euclidean spaces, as well as all of the Gr¨unbaum–Dress polyhedra, possess Petrie schemes that are not self-intersecting and thus have Petrie polygons that are simple closed curves. Partial results are obtained for several other classes of less symmetric polytopes.
The Gelfond–Schnirelman Method in Prime Number Theory
Authors: Pritsker Igor E.
Published: December 2010

The original Gelfond–Schnirelman method, proposed in 1936, uses polynomials with integer coefficients and small norms on [0, 1] to give a Chebyshev-type lower bound in prime number theory. We study a generalization of thismethod for polynomials inmany variables. Ourmain result is a lower bound for the integral of Chebyshev'sψ-function, expressed in terms of the weighted capacity. This extends previous work of Nair and Chudnovsky, and connects the subject to the potential theory with external fields generated by polynomial-type weights. We also solve the corresponding potential theoretic problem, by finding the extremal measure and its support.
On 𝒞ℛ-Epic Embeddings and Absolute 𝒞ℛ-Epic Spaces
Authors: Barr Michael , Raphael R. , Woods R. G.
Published: December 2010

We study Tychonoff spaces X with the property that, for all topological embeddings X → Y, the induced map C(Y ) → C(X) is an epimorphism of rings. Such spaces are called absolute 𝒞ℛ-epic. The simplest examples of absolute 𝒞ℛ-epic spaces are σ-compact locally compact spaces and Lindelöf P-spaces. We show that absolute CR-epic first countable spaces must be locally compact.

However, a “bad” class of absolute CR-epic spaces is exhibited whose pathology settles, in the negative, a number of open questions. Spaces which are not absolute CR-epic abound, and some are presented.
Asymptotic Behavior of the Length of Local Cohomology
Authors: Cutkosky Steven Dale , Hà Huy Tài , Srinivasan Hema , Theodorescu Emanoil
Published: December 2010

Let k be a field of characteristic 0, R = k[x1, … , xd] be a polynomial ring, and m its maximal homogeneous ideal. Let I ⊂ R be a homogeneous ideal in R. Let λ(M) denote the length of an Rmodule M. In this paper, we show that

always exists. This limit has been shown to be e(I)/d! form-primary ideals I in a local Cohen–Macaulay ring, where e(I) denotes the multiplicity of I. But we find that this limit may not be rational in general. We give an example for which the limit is an irrational number thereby showing that the lengths of these extension modules may not have polynomial growth.
Reciprocity Law for Compatible Systems of Abelian mod p Galois Representations
Authors: Khare Chandrashekhar
Published: December 2010

The main result of the paper is a reciprocity law which proves that compatible systems of semisimple, abelianmod p representations (of arbitrary dimension) of absolute Galois groups of number fields, arise from Hecke characters. In the last section analogs for Galois groups of function fields of these results are explored, and a question is raised whose answer seems to require developments in transcendence theory in characteristic p.
Generalized Reductive Lie Algebras: Connections With Extended Affine Lie Algebras and Lie Tori
Authors: Azam Saeid
Published: December 2010

We investigate a class of Lie algebras which we call generalized reductive Lie algebras. These are generalizations of semi-simple, reductive, and affine Kac–Moody Lie algebras. A generalized reductive Lie algebra which has an irreducible root system is said to be irreducible and we note that this class of algebras has been under intensive investigation in recent years. They have also been called extended affine Lie algebras. The larger class of generalized reductive Lie algebras has not been so intensively investigated. We study themin this paper and note that one way they arise is as fixed point subalgebras of finite order automorphisms. We show that the core modulo the center of a generalized reductive Lie algebra is a direct sum of centerless Lie tori. Therefore one can use the results known about the classification of centerless Lie tori to classify the cores modulo centers of generalized reductive Lie algebras.
Connections on a Parabolic Principal Bundle Over a Curve
Authors: Biswas Indranil
Published: December 2010

The aim here is to define connections on a parabolic principal bundle. Some applications are given.
Extension Theorems on Weighted Sobolev Spaces and Some Applications
Authors: Chua Seng-Kee
Published: December 2010

We extend the extension theorems to weighted Sobolev spaces on (ε, δ) domains with doubling weight w that satisfies a Poincaré inequality and such that w–1/p is locally Lp′. We also make use of the main theorem to improve weighted Sobolev interpolation inequalities.
Hypoelliptic Bi-Invariant Laplacians on Infinite Dimensional Compact Groups
Authors: Bendikov A. , Saloff-Coste L.
Published: December 2010

On a compact connected group G, consider the infinitesimal generator –L of a central symmetric Gaussian convolution semigroup (μt)t>0. Using appropriate notions of distribution and smooth function spaces, we prove that L is hypoelliptic if and only if (μt)t>0 is absolutely continuous with respect to Haar measure and admits a continuous density x ⟼ μt (x), t > 0, such that limt!0t log μt(e) = 0. In particular, this condition holds if and only if any Borel measure u which is solution of Lu = 0 in an open set Ω can be represented by a continuous function in Ω. Examples are discussed.
Decomposability of von Neumann Algebras and the Mazur Property of Higher Level
Authors: Hu Zhiguo , Neufang Matthias
Published: December 2010

The decomposability number of a von Neumann algebra ℳ (denoted by dec(ℳ)) is the greatest cardinality of a family of pairwise orthogonal non-zero projections in ℳ. In this paper, we explore the close connection between dec(ℳ) and the cardinal level of the Mazur property for the predual ℳ* of ℳ, the study of which was initiated by the second author. Here, our main focus is on those von Neumann algebras whose preduals constitute such important Banach algebras on a locally compact group G as the group algebra L1(G), the Fourier algebra A(G), the measure algebra M(G), the algebra LUC(G)*, etc. We show that for any of these von Neumann algebras, say ℳ, the cardinal number dec(ℳ) and a certain cardinal level of the Mazur property of ℳ* are completely encoded in the underlying group structure. In fact, they can be expressed precisely by two dual cardinal invariants of G: the compact covering number κ(G) of G and the least cardinality ᙭(G) of an open basis at the identity of G. We also present an application of the Mazur property of higher level to the topological centre problem for the Banach algebra A(G)**.
On the Cohomology of Moduli of Vector Bundles and the Tamagawa Number of SLn
Authors: Dhillon Ajneet
Published: December 2010

We compute some Hodge and Betti numbers of the moduli space of stable rank r, degree d vector bundles on a smooth projective curve. We do not assume r and d are coprime. In the process we equip the cohomology of an arbitrary algebraic stack with a functorial mixed Hodge structure. This Hodge structure is computed in the case of the moduli stack of rank r, degree d vector bundles on a curve. Our methods also yield a formula for the Poincaré polynomial of the moduli stack that is valid over any ground field. In the last section we use the previous sections to give a proof that the Tamagawa number of SLn is one.
Partial *-Automorphisms, Normalizers, and Submodules in Monotone Complete C*-Algebras
Authors: Hamana Masamichi
Published: December 2010

For monotone complete C*-algebras A ⊂ B with A contained in B as a monotone closed C*-subalgebra, the relation X = AsA gives a bijection between the set of all monotone closed linear subspaces X of B such that AX + XA ⊂ X and XX* + X*X ⊂ A and a set of certain partial isometries s in the “normalizer” of A in B, and similarly for the map s ⟼ Ad s between the latter set and a set of certain “partial *-automorphisms” of A. We introduce natural inverse semigroup structures in the set of such X's and the set of partial *-automorphisms of A, modulo a certain relation, so that the composition of these maps induces an inverse semigroup homomorphism between them. For a large enough B the homomorphism becomes surjective and all the partial *-automorphisms of A are realized via partial isometries in B. In particular, the inverse semigroup associated with a type II1 von Neumann factor, modulo the outer automorphism group, can be viewed as the fundamental group of the factor. We also consider the C*-algebra version of these results.
On Certain Classes of Unitary Representations for Split Classical Groups
Authors: Muić Goran
Published: December 2010

In this paper we prove the unitarity of duals of tempered representations supported onminimal parabolic subgroups for split classical p-adic groups. We also construct a family of unitary spherical representations for real and complex classical groups.
Growth and Zeros of the Zeta Function for Hyperbolic Rational Maps
Authors: Christianson Hans
Published: December 2010

This paper describes new results on the growth and zeros of the Ruelle zeta function for the Julia set of a hyperbolic rational map. It is shown that the zeta function is bounded by exp(CK|s|δ) in strips | Res| ≤K, whereδis the dimension of the Julia set. This leads to bounds on the number of zeros in strips (interpreted as the Pollicott–Ruelle resonances of this dynamical system). An upper bound on the number of zeros in polynomial regions {| Res| ≤ | Ims|α} is given, followed by weaker lower bound estimates in strips {Res> –C, | Ims| ≤r}, and logarithmic neighbourhoods {| Res| ≤ ρlog | Ims|}. Recent numerical work of Strain–Zworski suggests the upper bounds in strips are optimal.
Searching for Absolute ᘓℛ–Epic Spaces
Authors: Barr Michael , Kennison John F. , Raphael R.
Published: December 2010

In previous papers, Barr and Raphael investigated the situation of a topological space Y and a subspace X such that the induced map C(Y ) → C(X) is an epimorphism in the category ᘓℛ of commutative rings (with units). We call such an embedding a ᘓℛ-epic embedding and we say that X is absolute ᘓℛ-epic if every embedding of X is ᘓℛ-epic. We continue this investigation. Our most notable result shows that a Lindelöf space X is absolute ᘓℛ-epic if a countable intersection of βX-neighbourhoods of X is a βX-neighbourhood of X. This condition is stable under countable sums, the formation of closed subspaces, cozero-subspaces, and being the domain or codomain of a perfect map. A strengthening of the Lindelöf property leads to a new class with the same closure properties that is also closed under finite products. Moreover, all σ-compact spaces and all Lindelöf P-spaces satisfy this stronger condition. We get some results in the non-Lindelöf case that are sufficient to show that the Dieudonné plank and some closely related spaces are absolute ᘓℛ-epic.
Osculating Varieties of Veronese Varieties and Their Higher Secant Varieties
Authors: Bernardi A. , Catalisano M. V. , Gimigliano A. , Idà M.
Published: December 2010

We consider the k-osculating varieties Ok,n.d to the (Veronese) d-uple embeddings of ℙn. We study the dimension of their higher secant varieties via inverse systems (apolarity). By associating certain 0-dimensional schemes Y ⊂ ℙn to and by studying their Hilbert functions, we are able, in several cases, to determine whether those secant varieties are defective or not.
Cyclic Groups and the Three Distance Theorem
Authors: Chevallier Nicolas
Published: December 2010

We give a two dimensional extension of the three distance theorem. Let θ be in R2 and let q be in N. There exists a triangulation of R2 invariant by Z2-translations, whose set of vertices is Z2 + ﹛0, θ, … , qθ﹜, and whose number of different triangles, up to translations, is bounded above by a constant which does not depend on θ and q.
Preduals and Nuclear Operators Associated with Bounded, p-Convex, p-Concave and Positive p-Summing Operators
Authors: Labuschagne C. C. A.
Published: December 2010

We use Krivine's form of the Grothendieck inequality to renorm the space of bounded linear maps acting between Banach lattices. We construct preduals and describe the nuclear operators associated with these preduals for this renormed space of bounded operators as well as for the spaces of p-convex, p-concave and positive p-summing operators acting between Banach lattices and Banach spaces. The nuclear operators obtained are described in terms of factorizations through classical Banach spaces via positive operators.
Geometry and Spectra of Closed Extensions of Elliptic Cone Operators
Authors: Gil Juan B. , Krainer Thomas , Mendoza Gerardo A.
Published: December 2010

We study the geometry of the set of closed extensions of index 0 of an elliptic differential cone operator and its model operator in connection with the spectra of the extensions, and we give a necessary and sufficient condition for the existence of rays of minimal growth for such operators.
The Choquet–Deny Equation in a Banach Space
Authors: Jaworski Wojciech , Neufang Matthias
Published: December 2010

Let G be a locally compact group and π a representation of G by weakly* continuous isometries acting in a dual Banach space E. Given a probability measure μ on G, we study the Choquet–Deny equation π(μ)x = x, x ∈ E. We prove that the solutions of this equation form the range of a projection of norm 1 and can be represented by means of a “Poisson formula” on the same boundary space that is used to represent the bounded harmonic functions of the random walk of law μ. The relation between the space of solutions of the Choquet–Deny equation in E and the space of bounded harmonic functions can be understood in terms of a construction resembling theW*-crossed product and coinciding precisely with the crossed product in the special case of the Choquet–Deny equation in the space E = B(L2(G)) of bounded linear operators on L2(G). Other general properties of the Choquet–Deny equation in a Banach space are also discussed.
Ideas from Zariski Topology in the Study of Cubical Homology
Authors: Kaczynski Tomasz , Mrozek Marian , Trahan Anik
Published: December 2010

Cubical sets and their homology have been used in dynamical systems as well as in digital imaging. We take a fresh look at this topic, following Zariski ideas from algebraic geometry. The cubical topology is defined to be a topology in ℝd in which a set is closed if and only if it is cubical. This concept is a convenient frame for describing a variety of important features of cubical sets. Separation axioms which, in general, are not satisfied here, characterize exactly those pairs of points which we want to distinguish. The noetherian property guarantees the correctness of the algorithms. Moreover, maps between cubical sets which are continuous and closed with respect to the cubical topology are precisely those for whom the homology map can be defined and computed without grid subdivisions. A combinatorial version of the Vietoris–Begle theorem is derived. This theorem plays the central role in an algorithm computing homology of maps which are continuous with respect to the Euclidean topology.
Sobolev Extensions of Hölder Continuous and Characteristic Functions on Metric Spaces
Authors: Björn Anders , Björn Jana , Shanmugalingam Nageswari
Published: December 2010

We study when characteristic and Hölder continuous functions are traces of Sobolev functions on doubling metric measure spaces. We provide analytic and geometric conditions sufficient for extending characteristic and Hölder continuous functions into globally defined Sobolev functions.