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作者：Poltoratski, A.
摘要：Let mu be a finite positive measure on the real line. For a > 0, denote by epsilon(a) the family of exponential functions epsilon(a) - {epsilon(ist) vertical bar s is an element of[0, a]}. The exponential type of mu is the infimum of all numbers a such that the finite linear combinations of the exponentials from epsilon(a) are dense in L-2 (mu). If the set of such a is empty, the exponential type of mu is defined as infinity. The well-known type problem asks to find the exponential type of mu ...
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作者：Bezrukavnikov, Roman; Mirkovic, Ivan
摘要：We prove most of Lusztig's conjectures on the canonical basis in homology of a Springer fiber. The conjectures predict that this basis controls numerics of representations of the Lie algebra of a semisimple algebraic group over an algebraically closed field of positive characteristic. We check this for almost all characteristics. To this end we construct a noncommutative resolution of the nilpotent cone which is derived equivalent to the Springer resolution. On the one hand, this noncommutativ...
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作者：Maris, Mihai
摘要：For a large class of nonlinear Schrodinger equations with nonzero conditions at infinity and for any speed c less than the sound velocity, we prove the existence of nontrivial finite energy traveling waves moving with speed c in any space dimension N >= 3. Our results are valid as well for the Gross-Pitaevskii equation and for NLS with cubic-quintic nonlinearity.
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作者：Sela, Z.
摘要：This paper is the eighth in a sequence on the structure of sets of solutions to systems of equations in free and hyperbolic groups, projections of such sets (Diophantine sets), and the structure of definable sets over free and hyperbolic groups. In this eighth paper we use a modification of the sieve procedure, which was used in proving quantifier elimination in the theory of a free group, to prove that free and torsion-free (Gromov) hyperbolic groups are stable.
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作者：Klagsbrun, Zev; Mazur, Barry; Rubin, Karl
摘要：We study the parity of 2-Selmer ranks in the family of quadratic twists of an arbitrary elliptic curve E over an arbitrary number field K . We prove that the fraction of twists (of a given elliptic curve over a fixed number field) having even 2-Selmer rank exists as a stable limit over the family of twists, and we compute this fraction as an explicit product of local factors. We give an example of an elliptic curve E such that as K varies, these fractions are dense in [0,1] . More generally, o...
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作者：Bridgeland, Tom
摘要：We describe quantum enveloping algebras of symmetric Kac-Moody Lie algebras via a finite field Hall algebra construction involving Z(2)-graded complexes of quiver representations.
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作者：Keller, Bernhard
摘要：We prove the periodicity conjecture for pairs of Dynkin diagrams using Fomin-Zelevinsky's cluster algebras and their (additive) categorification via triangulated categories.
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作者：Bux, Kai-Uwe; Koehl, Ralf; Witzel, Stefan
摘要：We show that the finiteness length of an S-arithmetic subgroup Gamma in a noncommutative isotropic absolutely almost simple group G over a global function field is one less than the sum of the local ranks of G taken over the places in S. This determines the finiteness properties for arithmetic subgroups in isotropic reductive groups, confirming the conjectured finiteness properties for this class of groups. Our main tool is Behr-Harder reduction theory which we recast in terms of the metric st...
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作者：Kassabov, Martin; Pak, Igor
摘要：We construct an uncountable family of finitely generated groups of intermediate growth, with growth functions of new type. These functions can have large oscillations between lower and upper bounds, both of which come from a wide class of functions. In particular, we can have growth oscillating between e(n alpha) and any prescribed function, growing as rapidly as desired. Our construction is built on top of any of the Grigorchuk groups of intermediate growth and is a variation on the limit of ...
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作者：Miller, Stephen D.
摘要：Arthur has conjectured that the unitarity of a number of representations can be shown by finding appropriate automorphic realizations. This has been verified for classical groups by Moeglin and for the exceptional Chevalley group G(2) by Kim. In this paper we extend their results on spherical representations to the remaining exceptional groups E-6, E-7, E-8, and F-4. In particular, we prove Arthur's conjecture that the spherical constituent of an unramified principal series of a Chevalley grou...
