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作者：Elias, Ben; Williamson, Geordie
摘要：We prove Soergel's conjecture on the characters of indecomposable Soergel bimodules. We deduce that Kazhdan-Lusztig polynomials have positive coefficients for arbitrary Coxeter systems. Using results of Soergel one may deduce an algebraic proof of the Kazhdan-Lusztig conjecture.
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作者：Browning, T. D.; Matthiesen, L.; Skorobogatov, A. N.
摘要：For any pencil of conics or higher-dimensional quadrics over Q, with all degenerate fibres defined over Q, we show that the Brauer-Manin obs truction controls weak approximation. The proof is based on the Hasse principle and weak approximation for some special intersections of quadrics overQ, which is a consequence of recent advances in additive combinatorics.
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作者：Kahle, Matthew
摘要：For every k >= 1, the k-th cohomology group H-k (X,Q) of the random flag complex X similar to X (n,p) passes through two phase transitions: one where it appears and one where it vanishes. We describe the vanishing threshold and show that it is sharp. Using the same spectral methods, we also find a sharp threshold for the fundamental group pi(1)(X) to have Kazhdan's property (T). Combining with earlier results, we obtain as a corollary that for every k >= 3, there is a regime in which the rando...
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作者：Viehmann, Eva
摘要：The aim of this article is to define and study a new invariant of elements of loop groups that is invariant under sigma-conjugation by a hyperspecial maxi mal open subgroup and that we call the truncation of level 1. We classify truncations of level 1 and describe their specialization behavior. Further m ore, we prove group-theoretic conditions for the set of sigma-conjugacy classes obtained from elements of a given truncation of level 1 and in particular for the generic sigma-conjugacy class ...
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作者：Bondarenko, Andriy; Radchenko, Danylo; Viazovska, Maryna
摘要：In this paper we prove the conjecture of Korevaar and Meyers: for each N >= c(d)t(d), there exists a spherical t-design in the sphere S-d consisting of N points, where c(d) is a constant depending only on d.
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作者：Israel, Arie
摘要：Let L-2,L-p(R-2) be the Sobolev space of real-valued functions on the plane whose Hessian belongs to L-p. For any finite subset E subset of R-2 and p > 2, let L-2,L-p(R-2)vertical bar(E) be the space of real-valued functions on E, equipped with the trace seminorm. In this paper we construct a bounded linear extension operator T : L-2,L-p(R-2)vertical bar(E) -> L-2,L-p(R-2). We also provide an explicit formula that approximates the L-2,L-p(R-2)vertical bar(E) trace seminorm.
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作者：Hausel, Tamas; Letellier, Emmanuel; Rodriguez-Villegas, Fernando
摘要：We give a cohomological interpretation of both the Kac polynomial and the refined Donaldson-Thomas-invariants of quivers. This interpretation yields a proof of a conjecture of Kac from 1982 and gives a new perspective on recent work of Kontsevich Soibelman. This is achieved by computing, via an arithmetic Fourier transform, the dimensions of the isotypical components of the cohomology of associated Nakajima quiver varieties under the action of a Weyl group. The generating function of the corre...
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作者：Ardakov, Konstantin; Wadsley, Simon
摘要：We prove that the canonical dimension of a coadmissible representation of a semisimple p-adic Lie group in a p-adic Banach space is either zero or at least half the dimension of a nonzero coadjoint orbit. To do this we establish analogues for p-adically completed enveloping algebras of Bernstein's inequality for modules over Weyl algebras, the Beilinson-Bernstein localisation theorem and Quillen's Lemma about the endomorphism ring of a simple module over an enveloping algebra.
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作者：Gurel-Gurevich, Ori; Nachmias, Asaf
摘要：We prove that any distributional limit of finite planar graphs in which the degree of the root has an exponential tail is almost surely recurrent. As a corollary, we obtain that the uniform infinite planar triangulation and quadrangulation (UIPT and UIPQ) are almost surely recurrent, resolving a conjecture of Angel, Benjamini and Schramm. We also settle another related problem of Benjamini and Schramm. We show that in any bounded degree, finite planar graph the probability that the simple rand...
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作者：Blanc, Jeremy; Furter, Jean-Philippe
摘要：We study the algebraic structure of the n-dimensional Cremona group and show that it is not an algebraic group of infinite dimension (id-group) if n >= 2. We describe the obstruction to this, which is of a topological nature. By contrast, we show the existence of a Euclidean topology on the Cremona group which extends that of its classical subgroups and makes it a topological group.
