Related papers: Representations of SO(3) and angular polyspectra
We describe an algorithm for the extraction of the angular power spectrum of an intensity field, such as the cosmic microwave background (CMB), from interferometer data. This new method, based on the gridding of interferometer visibilities…
This article describes the computation of cosmic microwave background anisotropies in a universe with multi-connected spatial sections and focuses on the implementation of the topology in standard CMB computer codes. The key ingredient is…
An algebraic description of basic discrete symmetries (space reversal P, time reversal T and their combination PT) is studied. Discrete subgroups of orthogonal groups of multidimensional spaces over the fields of real and complex numbers…
Topological and geometrical methods are used to calculate the pseudorotational part of the vibronic spectrum for an electronic triplet of an octahedral, tetrahedral, or icosahedral molecule. The calculations take into account the nontrivial…
Erratum: In our paper, we show that the spectral representation for isotropic two-component composites also applies to uniaxial polycrystals. We have learned that this result was, in fact, first conjectured by G.W. Milton. While our…
COBE has provided us with a whole-sky map of the CBR anisotropies. However, even if the noise level is negligible when the four year COBE data are available, the cosmic variance will prevent us from obtaining information about the Gaussian…
We present an overarching framework for stable spectral methods on a triangle, defined by a multivariate W-system and based on orthogonal polynomials on the triangle. Motivated by the Koornwinder orthogonal polynomials on the triangle, we…
We use the mathematical structure of group algebras and $H^{+}$-algebras for describing certain problems concerning the quantum dynamics of systems of angular momenta, including also the spin systems. The underlying groups are ${\rm SU}(2)$…
Induced representations of Brauer algebra $D_{f}(n)$ from $S_{f_{1}}\times S_{f_{2}}$ with $f_{1}+f_{2}=f$ are discussed. The induction coefficients (IDCs) or the outer-product reduction coefficients (ORCs) of $S_{f_{1}}\times…
Isolating cuspidal automorphic representations from the whole automorphic spectrum is a basic problem in the trace formula approach. For example, matrix coefficients of supercupidal representations can be used as test functions for this,…
We lift the constraint of a diagonal representation of the Hamiltonian by searching for square integrable bases that support an infinite tridiagonal matrix representation of the wave operator. The class of solutions obtained as such…
Given a hyper loop algebra over a non-algebraically closed field, we address multiplicity problems in the underlying abelian tensor category of finite-dimensional representations. Namely, we give formulas for the l-characters of the simple…
We develop a method of simulating the full quantum field dynamics of multi-mode multi-component Bose-Einstein condensates in a trap. We use the truncated Wigner representation to obtain a probabilistic theory that can be sampled. This…
We reconstruct the polarization sector of a bright polarization squeezed beam starting from a complete set of Stokes measurements. Given the symmetry that underlies the polarization structure of quantum fields, we use the unique SU(2)…
The representations of the Schr\"odinger group in one space dimension are explicitly constructed in the basis of the harmonic oscillator states. These representations are seen to involve matrix orthogonal polynomials in a discrete variable…
Cosmological models where spatial sections are the Poincar\'e dodecahedral space D have been recently invoked to give an account of the lower modes of the angular anisotropies of the cosmic microwave background. Further explorations of this…
Spherical spin random fields are used to model the Cosmic Microwave Background polarization, the study of which is at the heart of modern Cosmology and will be the subject of the LITEBIRD mission, in the 2030s. Its scope is to collect datas…
The finite Heisenberg group knows when the dimension of Hilbert space is a square number. Remarkably, it then admits a representation such that the entire Clifford group --- the automorphism group of the Heisenberg group --- is represented…
It is noted that two-by-two S-matrices in multilayer optics can be represented by the Sp(2) group whose algebraic property is the same as the group of Lorentz transformations applicable to two space-like and one time-like dimensions. It is…
This article deals with nonrelativistic study of a D-dimensional superintegrable system, which generalizes the ordinary isotropic oscillator system. The coefficients for the expansion between the hyperspherical and Cartesian bases…