Related papers: Quantum multiplication operators for Lagrangian an…
The purpose of this paper is to study cohomology and deformations of $\mathcal{O}$-operators on Lie triple systems. We define a cohomology of an $\mathcal{O}$-operator $T$ as the Lie-Yamaguti cohomology of a certain Lie triple system…
We derive orthogonality relations for discrete q-ultraspherical polynomials and their duals by means of operators of representations of the quantum algebra su_q(1,1). Spectra and eigenfunctions of these operators are found explicitly. These…
Let A_r be the minimal resolution of the cyclic quotient singularity C^2/Z_{r+1}. We study the equivariant quantum cohomology ring of the n-fold symmetric product stack [Sym^n(A_r)] of A_r. We calculate the operators of quantum…
Supersymmetric quantum mechanics has many applications, and typically uses a raising and lowering operator formalism. For one dimensional problems, we show how such raising and lowering operators may be generalized to include an arbitrary…
We set up a framework for discussing `$q$-analogues' of the usual covariant differential operators for hermitian symmetric spaces. This turns out to be directly related to the deformation quantization associated to quadratic algebras…
For bicovariant differential calculi on quantum matrix groups a generalisation of classical notions such as metric tensor, Hodge operator, codifferential and Laplace-Beltrami operator for arbitrary k-forms is given. Under some technical…
This thesis is devoted to the study of joint spectral multipliers for a system of pairwise commuting, self-adjoint left-invariant differential operators L_1,...,L_n on a connected Lie group G. Under the assumption that the algebra generated…
The ingoing and outgoing null expansions associated to a spatial 2-sphere are quantized in the spherically symmetric model of loop quantum gravity. It is shown that the resulting expansion operators are self-adjoint in the kinematical…
This article presents a natural extension of the tensor algebra. In addition to "left multiplications" by vectors, we can consider "derivations" by covectors as basic operators on this extended algebra. These two types of operators satisfy…
A semi-infinite weighted Hankel matrix with entries defined in terms of basic hypergeometric series is explicitly diagonalized as an operator on $\ell^{2}(\mathbb{N}_{0})$. The approach uses the fact that the operator commutes with a…
Let $E$ be a Banach function space on a probability measure space $(\Omega ,\Sigma,\mu).$ Let $X$ be a Banach space and $E(X)$ be the associated K\"{o}the-Bochner space. An operator on $E(X)$ is called a multiplication operator if it is…
We prove that the geometric Satake correspondence admits quantum corrections for minuscule Grassmannians of Dynkin types $A$ and $D$. We find, as a corollary, that the quantum connection of a spinor variety $OG(n,2n)$ can be obtained as the…
We define an elliptic version of the stable envelope of Maulik and Okounkov for the equivariant elliptic cohomology of cotangent bundles of Grassmannians. It is a version of the construction proposed by Aganagic and Okounkov and is based on…
We find presentations by generators and relations for the equivariant quantum cohomology of the Grassmannian. For these presentations, we also find determinantal formulae for the equivariant quantum Schubert classes. To prove this, we use…
The standard toolkit of operators to probe quanta of geometry in loop quantum gravity consists in area and volume operators as well as holonomy operators. New operators have been defined, in the U(N) framework for intertwiners, which allow…
It is proved that both oscillatory integral operators and fractional oscillatory integral operators are bounded on weighted Morrey spaces. The corresponding commutators generated by $BMO$ functions are also considered.
The relations between $L^{\pm}$ operators and the generators in the quantum enveloping algebras are studied. The $L^{\pm}$ operators for $U_{q}A_{N}$ and $U_{q}G_{2}$ algebras are explicitly expressed by the generators as examples.
A practical computation method to find the eigenvalues and eigenspinors of quantum mechanical Hamiltonian is presented. The method is based on reduction of the eigenvalue equation to well known geometric algebra rotor equation and,…
We describe GJMS-operators as linear combinations of compositions of natural second-order differential operators. These are defined in terms of Poincar\'e-Einstein metrics and renormalized volume coefficients. As special cases, we find…
We obtain a combinatorial expression for the coefficients of the boundary map of real isotropic and odd orthogonal Grassmannians providing a natural generalization of the formulas already obtained for Lagrangian and maximal isotropic…