Ixr(a)的有限型Ixor(a)的未定Weyl群

本文首先给出Kac-Moody代数IXr(a)的有限型IC or (a)的未定Weyl群的定义,然后对a≥5证明了不定型李代数IXr(a)的Weyl群W同构于有限型IXr(a)的未定Weyl群.     

IX_r(a)的有限型IX_r~°(a)的未定Weyl群

本文首先给出Kac-Moody代数IXr(a)的有限型I(?)r(a)的未定Weyl群的定义,然后对a≥5证明了不定型李代数,IXr(a)的Weyl群W同构于有限型I(?)r(a)的未定Weyl群.     

Weyl Spectrum of Upper Triangular Operator Matrices

This paper is concerned with general n × n upper-triangular operator matrices with given diagonal entries. The characterizations of perturbations of their left(resp. right) Weyl spectrum and Weyl spectrum are given, based on the space decomposition technique. Moreover, some sufficient and necessary conditions are given under which the left(resp. right) Weyl spectrum and the Weyl spectrum of such operator matrix, respectively, coincide with the union of the left(resp. right) Weyl spectrum and the Weyl spectrum of its diagonal entries.     

On generalized Weyl operators

The ``generalized Weyl' operators between two Hilbert spaces are taken to be those with closed range for which the null space and that of the adjoint are of equal Hilbert space dimension. We show that products of two of these which happen to have closed range, and finite rank perturbation of these, are also generalized Weyl.

     

Some Weyl Modules for Simple Algebraic Groups of Type B4 and D4

Let G be a simply connected, semisimple algebraic group of type B₄ or D₄ over an algebraically closed field of characteristic p > 0. We determine the characters of certain simple modules for these groups by calculating the composition factors of the Weyl modules.     

Sharp remainder estimates in the Weyl formula for the Neumann Laplacian on a class of planar regions

We obtain estimates for the counting function of the Neumann Laplacian on a planar domain bounded by the graph of a lower semicontinuous L₁-function. These estimates imply necessary and sufficient conditions for the validity of the classical one-term Weyl formula for the counting function and, under certain restrictions, give an order sharp remainder estimate in this formula.     

On the Weyl symbol of the resolvent of the harmonic oscillator

We compute the Weyl symbol of the resolvent of the harmonic oscillator and study its properties.     

*-Representations of Twisted Generalized Weyl Constructions

We study bounded and unbounded *-representations of Twisted Generalized Weyl Algebras and algebras similar to them for different choices of involutions.     

A Combinatorial Description of the Syzygies of Certain Weyl Modules

Abstract

A basis for the syzygies of the resolution of 3-rowed Weyl modules with at most one triple overlap presented by Buchsbaum and Rota (Buchsbaum D., Rota, G.-C. (1994). A new construction in homological algebra. Proc. Natl. Acad. Sci. 91:4115–4119.) is constructed using Letter-Place techniques. This basis is explicitly given by computing the image under the differential of a conveniently chosen subset of the canonical Letter-Place basis of each term in the resolution.     

Weighted inequalities for some one-sided operators

We give a characterization of the pairs of weights such that the Weyl fractional integral operator maps into weak , or . For the case we give necessary and sufficient conditions for the weak type of a maximal operator that includes as particular cases the Weyl fractional integral, the dual of the Hardy operator and the fractional one-sided maximal operator. As a consequence we give a new characterization of the pairs of weights for which the fractional one-sided maximal operator is bounded.

     

Rigidity of some Weyl manifolds with nonpositive sectional curvature

We provide a list of all locally metric Weyl connections with nonpositive sectional curvatures on two types of manifolds, -dimensional tori and with the standard conformal structures. For we prove that it carries no other Weyl connections with nonpositive sectional curvatures, locally metric or not. In the case of we prove the same in the more narrow class of integrable connections.

     

Gelfand–Kirillov dimension of generalized Weyl algebras (In memory of Guenter Rudolf Krause (1941–2015))

Given a generalized Weyl algebra A of degree 1 with the base algebra D, we prove that the difference of the Gelfand–Kirillov dimension of A and that of D could be any positive integer or infinity. Under mild conditions, this difference is exactly 1. As applications, we calculate the Gelfand–Kirillov dimensions of various algebras of interest, including the (quantized) Weyl algebras, ambiskew polynomial rings, noetherian (generalized) down-up algebras, iterated Ore extensions, quantum Heisenberg algebras, universal enveloping algebras of Lie algebras, quantum GWAs, etc.     

Titchmarsh-Sims-Weyl Theory for Complex Hamiltonian Systems

The paper extends to complex Hamiltonian systems previous workof the authors on the Sims extension of the Titchmarsh–Weyltheory for Sturm–Liouville equations with complex potentials,and analyses the spectral properties of associated non-self-adjointoperators. 2000 Mathematics Subject Classification 34B20, 34Lxx.     

Une Neutralisation Explicite de L'algèbre de Weyl Quantique Complétée

Soit p un nombre premier. Nous établissons l'existence de neutralisations de divers complétés de l'algèbre de Weyl quantique spécialisée en une racine de l'unité primitive d'ordre p (qui est “génériquement” une algèbre d'Azumaya) et donnons en particulier un énoncé de neutralisation explicite relevant celui construit en caractéristique p dans [3 Gros , M. , Le Stum , B. , Quiros , A. ( 2010 ). A Simpson correspondence in positive characteristic . Publ. RIMS Kyoto Univ. 46 : 1 – 35 .[Crossref], [Web of Science ®] , [Google Scholar]].

Let p be a prime number. We establish the existence of neutralizations of various completions of the quantum Weyl algebra specialized at a primitive root of unity of prime order p (which is “generically” an Azumaya algebra) and, in particular, we give a statement of explicit neutralization similar to the one built in characteristic p in [3 Gros , M. , Le Stum , B. , Quiros , A. ( 2010 ). A Simpson correspondence in positive characteristic . Publ. RIMS Kyoto Univ. 46 : 1 – 35 .[Crossref], [Web of Science ®] , [Google Scholar]].     

D_l和E_6型Weyl群的扭子群的扩群

本文决定了 Dl 和 E6 型 Weyl群扭子群的所有扩群 ,这为确定相应 Chevalley群扭子群的所有扩群奠定了基础 .     

Quasi-Weyl asymptotics of the spectrum of the vector Dirichlet problem

In a space of vector functions, we consider the spectral problem

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, where

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, and the a _αjk and p _jk are constants, x ∈ Ω, and Ω is a bounded open set. The boundary conditions correspond to the Dirichlet problem. Let N _±(μ) be the positive and negative spectral counting functions. We establish the asymptotics N _±(μ) ～ (mes_mΩ)φ_±(μ) as μ → +0. The functions φ_±(μ) are independent of Ω. In the nonelliptic case, these asymptotics are in general different from the classical (Weyl) asymptotics.

     

Weyl quantization of Lebesgue spaces

We study boundedness and compactness properties for the Weyl quantization with symbols in L^q (?^2d ) acting on L^p (?^d ). This is shown to be equivalent, in suitable Banach space setting, to that of the Wigner transform. We give a short proof by interpolation of Lieb's sufficient conditions for the boundedness of the Wigner transform, proving furthermore that these conditions are also necessary. This yields a complete characterization of boundedness for Weyl operators in L^p setting; compactness follows by approximation. We extend these results defining two scales of spaces, namely L_*^q (?^2d ) and L_?^q (R^2d ), respectively smaller and larger than the L^q (?^2d ),and showing that the Weyl correspondence is bounded on L_*^q (R^2d ) (and yields compact operators), whereas it is not on L_?^q (R^2d ). We conclude with a remark on weak‐type L^p boundedness (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Homotopies for the Generalized Bar Complex Associated to Certain 3-Rowed Weyl Modules

In Buchsbaum and Rota (1994 Buchsbaum , D. , Rota , G.-C. ( 1994 ). A new construction in homological algebra . Proc. Nat. Acad. Sci. 91 : 4115 – 4119 . [CSA] [CROSSREF] [Crossref], [PubMed], [Web of Science ®] , [Google Scholar]), the authors presented a generalized bar complex associated to certain 3-rowed Weyl modules and proved that this complex is in fact a resolution via an induction on the number of overlaps between the second and third rows and a fundamental exact sequence (Akin and Buchsbaum, 1985 Akin , K. , Buchsbaum , D. ( 1985 ). Characteristic-free representation theory of the general linear group . Adv. Math 58 ( 2 ): 149 – 200 . [CSA]  [Google Scholar]). In this article we study the structure of this resolution by constructing a splitting contracting homotopy for the complexes corresponding to certain shapes.     

Weyl-Titchmarsh theory for symplectic difference systems

In this work, we establish Weyl-Titchmarsh theory for symplectic difference systems. This paper extends classical Weyl-Titchmarsh theory and provides a foundation for studying spectral theory of symplectic difference systems.