相关论文: Functions on Symmetric Spaces and Oscillator Repre…
Spherical representations and functions are the building blocks for harmonic analysis on riemannian symmetric spaces. In this paper we consider spherical functions and spherical representations related to certain infinite dimensional…
We investigate the summability in sense of Cesaro and its applications to investigation of the mean values of multiplicative functions on permutations.
We realize the Weil representation of infinite dimensional symplectic group and spinor representation of infinite-dimensional group $GL$ by linear operators in the space of symmetric functions in infinite number of variables.
In this paper we study the zeta functions associated to the minimal spherical principal series of representations for a class of reductive p-adic symmetric spaces, which are realized as open orbits of some prehomogeneous spaces. These…
This research focuses on the possibility of the surjective relation between symmetric potential function and its scattering matrix in 1-dimension. The theory bases on the property of wave function symmetry and boundary conditions. This…
Global invertible symmetries act unitarily on local observables or states of a quantum system. In this note, we aim to generalise this statement to non-invertible symmetries by considering unitary actions of higher fusion category…
We show that spherical Whittaker functions on an $n$-fold cover of the general linear group arise naturally from the quantum Fock space representation of $U_q(\widehat{\mathfrak{sl}}(n))$ introduced by Kashiwara, Miwa and Stern (KMS). We…
By applying methods already discussed in a previous series of papers by the same authors, we construct here classes of integrable quantum systems which correspond to n fully resonant oscillators with nonlinear couplings. The same methods…
In this paper some concepts of convex analysis on hyperbolic space are studied. We first study properties of the intrinsic distance, for instance, we present the spectral decomposition of its Hessian. Next, we study the concept of convex…
The main object of the present paper is to, introduce the. class of meromorphic univalent functions Involving! hypergeomatrc function .We obtain~ some interesting geometric properties according to coefficient inequality , growth and…
A general theory of matrix-spherical functions for dual Hopf algebras and right coideal subalgebras is developed. We establish their existence and define their orthogonality relations. When specialized to Kolb and Letzter's quantum…
A class of quantum analogues of compact symmetric spaces of classical type is introduced by means of constant solutions to the reflection equations. Their zonal spherical functions are discussed in connection with $q$-orthogonal…
We find a combinatorial formula for the Haar functional of the orthogonal and unitary quantum groups. As an application, we consider diagonal coefficients of the fundamental representation, and we investigate their spectral measures.
Family of replica matrices, related to general ultrametric spaces, is introduced. These matrices generalize the known Parisi matrices. Some functionals of replica approach are computed.
Consider the algebra Q<<x_1,x_2,...>> of formal power series in countably many noncommuting variables over the rationals. The subalgebra Pi(x_1,x_2,...) of symmetric functions in noncommuting variables consists of all elements invariant…
Bases for SU(3) irreps are constructed on a space of three-particle tensor products of two-dimensional harmonic oscillator wave functions. The Weyl group is represented as the symmetric group of permutations of the particle coordinates of…
We introduce and study properties of certain new harmonic function spaces on products of upper half-spaces.Norm estimates for the so-called expanded Bergman projections are obtained.Sharp theorems on multipliers acting on certain Sobolev…
This paper is devoted to the study of symplectic manifolds and their connection with Hamiltonian dynamical systems. We review some properties and operations on these manifolds and see how they intervene when studying the complete…
We prove a characterization of some $L^p$-Sobolev spaces involving the quadratic symmetrization of the Calder\'on commutator kernel, which is related to a square function with differences of difference quotients. An endpoint weak type…
Rotation representations are foundational in fields such as computer graphics, robotics, and machine learning, where precise and efficient modeling of 3D orientations is critical. This paper comprehensively investigates diverse…