bluuebunny/crossref_metadata_2025_split huggingface dataset:
Sufficiently Homogeneous Closed Embeddings of 𝔸n-1 into 𝔸n are Linear
Authors: Russell Peter 
Published: December 2010

AbstractWe show that over a field k of characteristic zero an affine (n — 1)- space embedded as a closed subvariety in affine n-space and homogeneous for a codimension two linear torus action on is defined by the vanishing of a variable.
Orthogonal Polynomials for a Family of Product Weight Functions on the Spheres
Authors: Xu Yuan 
Published: December 2010

AbstractBased on the theory of spherical harmonics for measures invariant under a finite reflection group developed by Dunkl recently, we study orthogonal polynomials with respect to the weight functions |x1|α1 . . . |xd|αd on the unit sphere Sd-1 in ℝd. The results include explicit formulae for orthonormal polynomials, reproducing and Poisson kernel, as well as intertwining operator.
Some Summation Theorems and Transformations for Q-Series
Authors: Ismail Mourad E. H. , Rahman Mizan , Suslov Sergei K. 
Published: December 2010

AbstractWe introduce a double sum extension of a very well-poised series and extend to this the transformations of Bailey and Sears as well as the 6ϕ5 summation formula of F. H. Jackson and the q-Dixon sum. We also give q-integral representations of the double sum. Generalizations of the Nassrallah-Rahman integral are also found.
The Schreier Technique for Subalgebras of a Free Lie Algebra
Authors: Rosset Shmuel , Wasserman Alon 
Published: December 2010

AbstractIn group theory Schreier's technique provides a basis for a subgroup of a free group. In this paper an analogue is developed for free Lie algebras. It hinges on the idea of cutting a Hall set into two parts. Using it, we show that proper subalgebras of finite codimension are not finitely generated and, following M. Hall, that a finitely generated subalgebra is a free factor of a subalgebra of finite codimension.
Fine Spectra and Limit Laws, II First-Order 0–1 Laws
Authors: Burris Stanley , Kevin Compton  , Odlyzko Andrew , Richmond Bruce 
Published: December 2010

AbstractUsing Feferman-Vaught techniques a condition on the fine spectrum of an admissible class of structures is found which leads to a first-order 0–1 law. The condition presented is best possible in the sense that if it is violated then one can find an admissible class with the same fine spectrum which does not have a first–order 0–1 law.If the condition is satisfied (and hence we have a first-order 0–1 law) we give a natural model of the limit law theory; and show that the limit law theory is decidable if the theory of the directly indecomposables is decidable. Using asymptotic methods from the partition calculus a useful test is derived to show several admissible classes have a first–order 0–1 law.
Rational Classification of Simple Function Space Components for Flag Manifolds
Authors: Smith Samuel Bruce 
Published: December 2010

AbstractLetM(X, Y) denote the space of all continuous functions between X and Y and Mƒ(X, Y) the path component corresponding to a given map ƒ : X → Y. When X and Y are classical flag manifolds, we prove the components of M(X, Y) corresponding to “simple” maps ƒ are classified up to rational homotopy type by the dimension of the kernel of ƒ in degree two cohomology. In fact, these components are themselves all products of flag manifolds and odd spheres.
Polynomials With {0, +1, -1} Coefficients and a Root Close to a Given Point
Authors: Borwein Peter , Pinner Christopher 
Published: December 2010

AbstractFor a fixed algebraic number α we discuss how closely α can be approximated by a root of a {0, +1, -1} polynomial of given degree. We show that the worst rate of approximation tends to occur for roots of unity, particularly those of small degree. For roots of unity these bounds depend on the order of vanishing, k, of the polynomial at α.In particular we obtain the following. Let BN denote the set of roots of all {0, +1, -1} polynomials of degree at most N and BN(α k) the roots of those polynomials that have a root of order at most k at α. For a Pisot number α in (1, 2] we show thatand for a root of unity α thatWe study in detail the case of α = 1, where, by far, the best approximations are real. We give fairly precise bounds on the closest real root to 1. When k = 0 or 1 we can describe the extremal polynomials explicitly.
Quantization of the 4-Dimensional Nilpotent Orbit of Sl(3, ℝ)
Authors: Brylinski Ranee 
Published: December 2010

AbstractWe give a new geometric model for the quantization of the 4-dimensional conical (nilpotent) adjoint orbit Oℝof SL(3,ℝ). The space of quantization is the space of holomorphic functions on 𝕔2- {0}) which are square integrable with respect to a signed measure defined by a Meijer G-function. We construct the quantization out a non-flat Kaehler structure on 𝕔2- {0}) (the universal cover of Oℝ) with Kaehler potential ρ |z|4.
The Von Neumann Algebra VN(G) of a Locally Compact Group and Quotients of Its Subspaces
Authors: Hu Zhiguo 
Published: December 2010

AbstractLet VN(G) be the von Neumann algebra of a locally compact group G. We denote by μ the initial ordinal with |μ| equal to the smallest cardinality of an open basis at the unit of G and X = ﹛α ; α < μ﹜.We show that if G is nondiscrete then there exist an isometric *-isomorphism of l∞(X) into VN(G) and a positive linear mapping π of VN(G) onto l∞(X) such that π o = idl∞(X) and and π have certain additional properties. Let UCB((Ĝ)) be the C*–algebra generated by operators in VN(G) with compact support and F(Ĝ) the space of all T∈ VN(G) such that all topologically invariant means on VN(G) attain the same value at T. The construction of the mapping π leads to the conclusion that the quotient space UCB((Ĝ))/F((Ĝ)) ∪UCB((Ĝ)) has l∞(X) as a continuous linear image if G is nondiscrete. When G is further assumed to be non-metrizable, it is shown that UCB((Ĝ))/F((Ĝ)) ∪UCB((Ĝ)) contains a linear isomorphic copy of l∞(X). Similar results are also obtained for other quotient spaces.
Subalgebras Which Appear in Quantum Iwasawa Decompositions
Authors: Letzter Gail 
Published: December 2010

AbstractLet g be a semisimple Lie algebra. Quantum analogs of the enveloping algebra of the fixed Lie subalgebra are introduced for involutions corresponding to the negative of a diagram automorphism. These subalgebras of the quantized enveloping algebra specialize to their classical counterparts. They are used to form an Iwasawa type decompostition and begin a study of quantum Harish-Chandra modules.
Elementary Proof of the Fundamental Lemma For a Unitary Group
Authors: Flicker Yuval Z. 
Published: December 2010

AbstractThe fundamental lemma in the theory of automorphic forms is proven for the (quasi-split) unitary group U(3) in three variables associatedwith a quadratic extension of p-adic fields, and its endoscopic group U(2), by means of a new, elementary technique. This lemma is a prerequisite for an application of the trace formula to classify the automorphic and admissible representations of U(3) in terms of those of U(2) and base change to GL(3). It compares the (unstable) orbital integral of the characteristic function of the standard maximal compact subgroup K of U(3) at a regular element (whose centralizer T is a torus), with an analogous (stable) orbital integral on the endoscopic group U(2). The technique is based on computing the sum over the double coset space T\G/K which describes the integral, by means of an intermediate double coset space H\G/K for a subgroup H of G= U(3) containing T. Such an argument originates from Weissauer's work on the symplectic group. The lemma is proven for both ramified and unramified regular elements, for which endoscopy occurs (the stable conjugacy class is not a single orbit).
Inequalities for Rational Functions With Prescribed Poles
Authors: Min G. 
Published: December 2010

AbstractThis paper considers the rational system Pn(a1, a2,……,an) := with nonreal elements in paired by complex conjugation. It gives a sharp (to constant) Markov-type inequality for real rational functions in Pn(a1, a2,……an). The corresponding Markov-type inequality for high derivatives is established, as well as Nikolskii-type inequalities. Some sharp Markov- and Bernstein-type inequalities with curved majorants for rational functions in Pn(a1, a2,……an) are obtained, which generalize some results for the classical polynomials. A sharp Schur-type inequality is also proved and plays a key role in the proofs of our main results
Units in Group Rings of Free Products of Prime Cyclic Groups
Authors: Dokuchaev Michael A. , Sobral Singer Maria Lucia 
Published: December 2010

AbstractLet G be a free product of cyclic groups of prime order. The structure of the unit group U(ℚG) of the rational group ring ℚG is given in terms of free products and amalgamated free products of groups. As an application, all finite subgroups of U(ℚG), up to conjugacy, are described and the Zassenhaus Conjecture for finite subgroups in ℤ G is proved. A strong version of the Tits Alternative for U(ℚG) is obtained as a corollary of the structural result.
The Groups of the Regular Star-Polytopes
Authors: McMullen Peter 
Published: December 2010

AbstractThe regular star-polyhedron is isomorphic to the abstract polyhedron {5, 5,| 3}, where the last entry “3” in its symbol denotes the size of a hole, given by the imposition of a certain extra relation on the group of the hyperbolic honeycomb {5, 5}. Here, analogous formulations are found for the groups of the regular 4-dimensional star-polytopes, and for those of the non-discrete regular 4-dimensional honeycombs. In all cases, the extra group relations to be imposed on the corresponding Coxeter groups are those arising from “deep holes”; thus the abstract description of for k = 1 or 2. The non-discrete quasi-regular honeycombs in 𝔼3, on the other hand, are not determined in an analogous way.
Multipliers of Fractional Cauchy Transforms and Smoothness Conditions
Authors: Luo Donghan , Macgregor Thomas 
Published: December 2010

AbstractThis paper studies conditions on an analytic function that imply it belongs to Mα, the set of multipliers of the family of functions given by where μ is a complex Borel measure on the unit circle and α > 0. There are two main theorems. The first asserts that if 0 < α < 1 and sup. The second asserts that if 0 < α < 1, ƒ ∈ H∞ and supt. The conditions in these theorems are shown to relate to a number of smoothness conditions on the unit circle for a function analytic in the open unit disk and continuous in its closure.
Fractals in the Large
Authors: Strichartz Robert S. 
Published: December 2010

AbstractA reverse iterated function system (r.i.f.s.) is defined to be a set of expansive maps ﹛T1,…, Tm﹜ on a discrete metric space M. An invariant set F is defined to be a set satisfying , and an invariant measure μ is defined to be a solution of for positive weights pj. The structure and basic properties of such invariant sets and measures is described, and some examples are given. A blowup ℱ of a self-similar set F in ℝn is defined to be the union of an increasing sequence of sets, each similar to F. We give a general construction of blowups, and show that under certain hypotheses a blowup is the sum set of F with an invariant set for a r.i.f.s. Some examples of blowups of familiar fractals are described. If μ is an invariant measure on ℤ+ for a linear r.i.f.s., we describe the behavior of its analytic transform, the power series on the unit disc.
Hankel Operators on Pseudoconvex Domains of Finite Type in ℂ2
Authors: Symesak Frédéric 
Published: December 2010

AbstractThe aimof this paper is to study small Hankel operatorshon the Hardy space or on weighted Bergman spaces,where Ω is a finite type domain in ℂ2or a strictly pseudoconvex domain in ℂn. We give a sufficient condition on the symbolƒso thathbelongs to the Schatten classSp, 1 ≤p< +∞.
Decomposition Varieties in Semisimple Lie Algebras
Authors: Broer Abraham 
Published: December 2010

AbstractThe notion of decompositon class in a semisimple Lie algebra is a common generalization of nilpotent orbits and the set of regular semisimple elements.We prove that the closure of a decomposition class has many properties in common with nilpotent varieties, e.g., its normalization has rational singularities.The famous Grothendieck simultaneous resolution is related to the decomposition class of regular semisimple elements. We study the properties of the analogous commutative diagrams associated to an arbitrary decomposition class.
Ward’s Solitons II: Exact Solutions
Authors: Anand Christopher Kumar 
Published: December 2010

AbstractIn a previous paper, we gave a correspondence between certain exact solutions to a (2 + 1)-dimensional integrable Chiral Model and holomorphic bundles on a compact surface. In this paper, we use algebraic geometry to derive a closed-form expression for those solutions and show by way of examples how the algebraic data which parametrise the solution space dictates the behaviour of the solutions.
A Lower Bound For KxL Of Quasi-Polarized Surfaces (X, L) With Non-Negative Kodaira Dimension
Authors: Fukuma Yoshiaki 
Published: December 2010

AbstractLet X be a smooth projective surface over the complex number field and let L be a nef-big divisor on X. Here we consider the following conjecture; If the Kodaira dimension ≥ 0, then KXL ≥ 2q(X) - 4, where q(X) is the irregularity of X. In this paper, we prove that this conjecture is true if (1) the case in which = 0 or 1, (2) the case in which = 2 and h0(L) ≥ 2, or (3) the case in which = 2, X is minimal, h0(L) = 1, and L satisfies some conditions.
The Dual Pair G2 × PU3 (D) (p-Adic Case)
Authors: Savin Gordan , Gan Wee Teck 
Published: December 2010

AbstractWe study the correspondence of representations arising by restricting the minimal representation of the linear group of type E7 and relative rank 4. The main tool is computations of the Jacquet modules of the minimal representation with respect to maximal parabolic subgroups of G2 and PU3(D).
Parabolic Subgroups with Abelian Unipotent Radical as a Testing Site for Invariant Theory
Authors: Panyushev Dmitri I. 
Published: December 2010

AbstractLet 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

AbstractUsing 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.
The Hausdorff and Packing Dimensions of Some Sets Related to Sierpiński Carpets
Authors: Nielsen Ole A. 
Published: December 2010

AbstractThe 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.
Sublinearity and Other Spectral Conditions on a Semigroup
Authors: Radjavi Heydar 
Published: December 2010

AbstractSubadditivity, 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

AbstractThis 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

AbstractSuppose 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

AbstractThe 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

AbstractThe ‘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).
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

AbstractThis 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

AbstractWe 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

AbstractLet 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

AbstractWe 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

AbstractLet 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

AbstractIn 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.