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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,...
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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...
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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...
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作者：Donagi, R.; Pantev, T.
作者单位：University of Pennsylvania
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作者：Belinschi, Serban; Collins, Benoit; Nechita, Ion
作者单位：University of Ottawa; University of Saskatchewan; Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet; Institute of Mathematics of the Romanian Academy; Romanian Academy
摘要：Given two positive integers n and k and a parameter ta(0,1), we choose at random a vector subspace V (n) aS,a, (k) aSua, (n) of dimension N similar to tnk. We show that the set of k-tuples of singular values of all unit vectors in V (n) fills asymptotically (as n tends to infinity) a deterministic convex set K (k,t) that we describe using a new norm in ae (k) . Our proof relies on free probability, random matrix theory, complex analysis and matrix analysis techniques. The main result comes tog...
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作者：Ein, Lawrence; Lazarsfeld, Robert
作者单位：University of Michigan System; University of Michigan; University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital
摘要：We study the asymptotic behavior of the syzygies of a smooth projective variety as the positivity of the embedding line bundle grows. The main result asserts that the syzygy modules are non-zero in almost all degrees allowed by Castelnuovo-Mumford regularity. We also give an effective statement for Veronese varieties that we conjecture to be optimal.
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作者：Gordon, I. G.
作者单位：University of Edinburgh; University of Edinburgh; Heriot Watt University
摘要：Using the Harish-Chandra D-module, we give a proof of Haiman's theorem on the positivity of Macdonald polynomials. Ginzburg's work on the connection between this D-module and the isospectral commuting variety is fundamental to this approach.
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作者：Pink, Richard
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We prove the isogeny conjecture for A-motives over finitely generated fields K of transcendence degree <= 1. This conjecture says that for any semisimple A-motive M over K, there exist only finitely many isomorphism classes of A-motives M' over K for which there exists a separable isogeny M' -> M. The result is in precise analogy to known results for abelian varieties and for Drinfeld modules and will have strong consequences for the p-adic and adelic Galois representations associated to M. Th...
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作者：Toen, Bertrand
作者单位：Universite de Montpellier
摘要：We introduce a notion of derived Azumaya algebras over ring and schemes generalizing the notion of Azumaya algebras of Grothendieck (Le groupe de Brauer. I. AlgSbres d'Azumaya et interpr,tations diverses. Dix Expos,s sur la Cohomologie des Sch,mas, pp. 46-66, North-Holland, Amsterdam, 1968). We prove that any such algebra B on a scheme X provides a class I center dot(B) in . We prove that for X a quasi-compact and quasi-separated scheme I center dot defines a bijective correspondence, and in p...
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作者：Tran Vu Khanh; Zampieri, Giuseppe
作者单位：University of Padua
摘要：We show the geometric and analytic consequences of a general estimate in the (partial derivative) over bar -Neumann problem: a gain in the estimate yields a bound in the type of the boundary, that is, in its order of contact with an analytic curve as well as in the rate of the Bergman metric. We also discuss the potential-theoretical consequence: a gain implies a lower bound for the Levi form of a bounded weight.
