Related papers: Continuity of magnetic Weyl calculus
We endow the group of automorphisms of an exact Courant algebroid over a compact manifold with an infinite dimensional Lie group structure modelled on the inverse limit of Hilbert spaces (ILH). We prove a slice theorem for the action of…
This paper investigates bicovariant differential calculus on noncommutative spaces of the Lie algebra type. For a given Lie algebra $g_0$ we construct a Lie superalgebra $g=g_0\oplus g_1$ containing noncommutative coordinates and…
We calculate the Weyl group invariants with respect to a maximal torus of the exceptional Lie group $E_6$.
We prove criteria for a {\it 'magnetic' Weyl operator} to be in a Schatten-von Neuman class by extending a method developed by H. Cordes, T. Kato and G. Arsu.
We discuss multi-graded nilpotent tuples of multi-graded vector spaces which are a generalization of graded nilpotent pairs. The multi-grading yields a natural notion of a shape of such tuple and our main interest is to answer the question…
The aim of this article is to find all weight modules of degree 1 of a simple complex Lie algebra that integrate to a continuous representation of a simply-connected real Lie group on some Hilbert space.
We investigate Weyl anomalies on a curved world sheet to second order in a weak field expansion. Using a local version of the exact renormalization group equations, we obtain nonperturbative results for the tachyon/graviton/dilaton system.…
There is a connection between the Weyl pseudodifferential calculus and crossed product C*-algebras associated with certain dynamical systems. And in fact both topics are involved in the quantization of a non-relativistic particle moving in…
In this paper we study the modulus of continuity of weak solutions to a singular elliptic equation in the plane under very weak assumption on the integrability of the elliptic coefficients. Our investigation reveals that the modulus of…
In this note we give a short and self-contained proof for a criterion of Eidelheit on the solvability of linear equations in infinitely many variables. We use this criterion to study the surjectivity of magnetic Schr\"odinger operators on…
In this paper we develop the functional calculus for elliptic operators on compact Lie groups without the assumption that the operator is a classical pseudo-differential operator. Consequently, we provide a symbolic descriptions of complex…
This paper studies extension groups between certain Weyl modules for the algebraic group GL_n over the integers. Main results include: (1) A complete determination of Ext groups between Weyl modules whose highest weights differ by a single…
Our goal is to classify all generically transitive actions of commutative unipotent groups on flag varieties up to conjugation. We establish relationship between this problem and classification of multiplications with certain properties on…
We introduce Morita equivalence for Nijenhuis groupoids and for their infinitesimal counterparts, establishing a global-to-infinitesimal correspondence under the Lie functor. A special case is that of holomorphic Lie groupoids and…
We define and examine certain matrix-valued multiplicative functionals with local Kato potential terms and use probabilistic techniques to prove that the semigroups of the corresponding partial differential operators with matrix-valued…
In this note we present some experimental results on the general matrix nilpotent Lie algebras derived by calculations on a computer
We give a condition ensuring that the operators in a nilpotent Lie algebra of linear operators on a finite dimensional vector space have a common eigenvector.
We compute the noncommutative deformations of a family of modules over the first Weyl algebra. This example shows some important properties of noncommutative deformation theory that separates it from commutative deformation theory.
In this article we prove a generalization of Weyl's criterion for the spectrum of a self-adjoint nonnegative operator on a Hilbert space. We will apply this new criterion in combination with Cheeger-Fukaya-Gromov and Cheeger-Colding theory…
We show continuity in generalized weighted Morrey spaces of sub-linear integral operators generated by some classical integral operators and commutators. The obtained estimates are used to study global regularity of the solution of the…