相关论文: Intertwinors on Differential Forms over the Produc…

We construct the rings of generalized differential operators on the ${\bf h}$-deformed vector space of ${\bf gl}$-type. In contrast to the $q$-deformed vector space, where the ring of differential operators is unique up to an isomorphism,…

We establish an isomorphism between the moduli space of homologically trivial parabolic (Higgs) bundles on $\mathbb{P}^1$ and the quiver variety associated to a star-shaped quiver. As applications, we deduce a closed formula for the…

We describe the structure of diffeological bundle of non formal classical pseudo-differential operators over formal ones, and its structure group. For this, we give few results on diffeological principal bundles with (a priori) no local…

In this paper, we enlarge the space of uniformly supported pseudo-differential operators on some groupoids by considering kernels satisfying certain asymptotic estimates. We show that such enlarged space contains the compact parametrix, and…

Let $G=SO_0(1,n)$ be the conformal group acting on the $(n-1)$ dimensional sphere $S$, and let $(\pi_\lambda)_{\lambda\in \mathbb C}$ be the spherical principal series. For generic values of $\boldsymbol \lambda…

We interpret tensors on a smooth manifold M as differential forms over a graded commutative algebra called the algebra of iterated differential forms over M. This allows us to put standard tensor calculus in a new differentially closed…

We introduce an $R$-matrix acting on the tensor product of MacMahon representations of Ding-Iohara-Miki (DIM) algebra $U_{q,t}(\widehat{\widehat{\mathfrak{gl}}}_1)$. This $R$-matrix acts on pairs of $3d$ Young diagrams and retains the nice…

We compute the number of linearly independent ways in which a tensor of Weyl type may act upon a given irreducible tensor-spinor bundle V over a Riemannian manifold. Together with the analogous but easier problem involving actions of…

Let $\sigma(x,\xi) $ be a sufficiently regular function defined on $R^d \times R^d.$ The pseudo-differential operator with symbol $\sigma$ is defined on the Schwartz class by the formula: \[f\to\sigma f(x)=\int_{R^d} \sigma(x,\xi)…

We develop a frame and dyad gauge-independent formalism for the calculus of variations of functionals involving spinorial objects. As part of this formalism we define a modified variation operator which absorbs frame and spin dyad gauge…

We construct algebras of pseudodifferential operators on a continuous family groupoid G that are closed under holomorphic functional calculus, contain the algebra of all pseudodifferential operators of order 0 on G as a dense subalgebra,…

In this work we produce microlocal normal forms for pseudodifferential operators which have a Lagrangian submanifold of radial points. This answers natural questions about such operators and their associated classical dynamics. In a sequel,…

The multilinear pseudo-differential operators with symbols in the multilinear H\"ormander class $S_{0,0}$ are considered. A complete identification of the cases where those operators define bounded operators between local Hardy spaces is…

In this article we give general neccessary and sufficient conditions to ensure that a pseudo-Riemannian manifold is conformal to an Einstein space. These conditions are algorithmic in \emph{the metric tensor} whenever the Weyl endomorphism…

We present a novel approach to the classification of conformally equivariant differential operators on spinors in the case of homogeneous conformal geometry. It is based on the classification of solutions for a vector-valued system of…

We construct an algebra of pseudodifferential operators on each groupoid in a class that generalizes differentiable groupoids to allow manifolds with corners. We show that this construction encompasses many examples. The subalgebra of…

Let $F$ be a finite extension of $\mathbb{Q}_p$, let $\Omega_F$ be Drinfeld's upper half-plane over $F$ and let $G^0$ the subgroup of $GL_2(F)$ consisting of elements whose determinant has norm $1$. By working locally on $\Omega_F$, we…

We discuss the essential spectrum of essentially self-adjoint elliptic differential operators of first order and of Laplace type operators on Riemannian vector bundles over geometrically finite orbifolds.

Let $M$ be a connected smooth manifold, let $\operatorname{Aut}(p)$ be the group automorphisms of the bundle $p\colon \mathbb{R}\times M\to \mathbb{R}$, and let $q\colon J^1(\mathbb{R},M)\times \mathbb{R\to }J^1(\mathbb{R},M)$ be the…

In differential geometry, geometric structures can often be encoded by differential forms satisfying algebraic and differential constraints. This is in particular the case for spinorial G-structures, where the defining tensors are…