Inventiones mathematicae

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• A fixed point theorem for L 1 spaces AI翻译
  作者：Bader, U.; Gelander, T.; Monod, N.
  作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Hebrew University of Jerusalem; Technion Israel Institute of Technology
  摘要：We prove a fixed point theorem for a family of Banach spaces including notably L (1) and its non-commutative analogues. Several applications are given, e.g. the optimal solution to the derivation problem studied since the 1960s.
• Thurston's pullback map on the augmented Teichmuller space and applications AI翻译
  作者：Selinger, Nikita
  作者单位：Constructor University
  摘要：Let f be a postcritically finite branched self-cover of a 2-dimensional topological sphere. Such a map induces an analytic self-map sigma (f) of a finite-dimensional Teichmuller space. We prove that this map extends continuously to the augmented Teichmuller space and give an explicit construction for this extension. This allows us to characterize the dynamics of Thurston's pullback map near invariant strata of the boundary of the augmented Teichmuller space. The resulting classification of inv...
• On characters and formal degrees of discrete series of affine Hecke algebras of classical types AI翻译
  作者：Ciubotaru, Dan; Kato (Shiota), Midori; Kato, Syu
  作者单位：Utah System of Higher Education; University of Utah; University of Tokyo; Kyoto University
  摘要：We address two fundamental questions in the representation theory of affine Hecke algebras of classical types. One is an inductive algorithm to compute characters of tempered modules, and the other is the determination of the constants in the formal degrees of discrete series (in the form conjectured by Reeder (J. Reine Angew. Math. 520:37-93, 2000)). The former is completely different from the Lusztig-Shoji algorithm (Shoji in Invent. Math. 74:239-267, 1983; Lusztig in Ann. Math. 131:355-408,...
• Invariant tori for the cubic Szego equation AI翻译
  作者：Gerard, Patrick; Grellier, Sandrine
  作者单位：Universite de Orleans; Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
  摘要：We continue the study of the following Hamiltonian equation on the Hardy space of the circle, i partial derivative(t)u = Pi(vertical bar u vertical bar(2)u), where Pi denotes the Szego projector. This equation can be seen as a toy model for totally non dispersive evolution equations. In a previous work, we proved that this equation admits a Lax pair, and that it is completely integrable. In this paper, we construct the action-angle variables, which reduces the explicit resolution of the equati...
• Generators and commutators in finite groups; abstract quotients of compact groups AI翻译
  作者：Nikolov, Nikolay; Segal, Dan
  作者单位：University of Oxford; Imperial College London
  摘要：The first part of the paper establishes results about products of commutators in a d-generator finite group G, for example: if HaS(2)G=aOE (c) g (1),aEuro broken vertical bar,g (r) > then every element of the subgroup [H,G] is a product of f(r) factors of the form with . Under certain conditions on H, a similar conclusion holds with the significantly weaker hypothesis that G=HaOE (c) g (1),aEuro broken vertical bar,g (r) >, where f(r) is replaced by f (1)(d,r). The results are applied in the s...
• Expansion in SLd(Z/qZ), q arbitrary AI翻译
  作者：Bourgain, Jean; Varju, Peter P.
  作者单位：Institute for Advanced Study - USA; Princeton University; Szeged University; Hungarian Academy of Sciences
  摘要：Let S be a fixed finite symmetric subset of SLd(Z), and assume that it generates a Zariski-dense subgroup G. We show that the Cayley graphs of pi(q)(G) with respect to the generating set pi(q)(S) form a family of expanders, where pi(q) is the projection map Z -> Z/qZ.
• Langlands duality for Hitchin systems AI翻译
  作者：Donagi, R.; Pantev, T.
  作者单位：University of Pennsylvania
• Nuclear dimension and Z-stability of pure C*-algebras AI翻译
  作者：Winter, Wilhelm
  作者单位：University of Nottingham
  摘要：In this article I study a number of topological and algebraic dimension type properties of simple C*-algebras and their interplay. In particular, a simple C*-algebra is defined to be (tracially) (m, m (m) over bar)-pure, if it has (strong tracial) m-comparison and is (tracially) (m) over bar -almost divisible. These notions are related to each other, and to nuclear dimension. The main result says that if a separable, simple, nonelementary, unital C*algebra with locally finite nuclear dimension...
• Growth of permutational extensions AI翻译
  作者：Bartholdi, Laurent; Erschler, Anna
  作者单位：University of Gottingen; Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay
  摘要：We study the geometry of a class of group extensions, containing permutational wreath products, which we call permutational extensions. We construct for all k is an element of N a torsion group K-k with growth function upsilon K-k (n) similar to exp(n(1-(1-alpha)k)), 2(3-3/alpha) + 2(2-2/alpha) + 2(1-1/alpha) = 2, and a torsion-free group H-k with growth function upsilon H-k (n) similar to exp(log(n)n(1-(1-alpha)k)). These are the first examples of groups of intermediate growth for which the a...
• Classification and nondegeneracy of SU(n+1) Toda system with singular sources AI翻译
  作者：Lin, Chang-Shou; Wei, Juncheng; Ye, Dong
  作者单位：National Taiwan University; Chinese University of Hong Kong; Universite de Lorraine
  摘要：We consider the following Toda system Delta u(i) + Sigma(n)(j=1)a(ij)e(uj) = 4 pi gamma(i)delta(0) in R-2, integral(R2)e(ui)dx < infinity, for all 1 <= i <= n, where gamma (i) >-1, delta (0) is Dirac measure at 0, and the coefficients a (ij) form the standard tri-diagonal Cartan matrix. In this paper, (i) we completely classify the solutions and obtain the quantization result: Sigma(n)(j=1)a(ij) integral(R2)e(uj)dx = 4 pi(2 + gamma(i) + gamma(n+1-i)), for all 1 <= i <= n This generalizes the c...