相关论文: Generator Matrix Elements For $G_2 \supset SU(3)$ …
A new set of polynomial states (to be called character states) are derived for $Sp(4)$ reduced to its $SU(2) \times U(1)$ subgroup, and the relevant generator matrix elements are evaluated for generic representations $(a,b)$ of $Sp(4)$.…
A general group element for the fundamental representation of SU(3) is expressed as a second order polynomial in the hermitian generating matrix H, with coefficients consisting of elementary trigonometric functions dependent on the sole…
A new set of polynomial states (to be called character states) are derived for $Sp(4)$ reduced to its $SU(2) \times U(1)$ subgroup, and the relevant generator matrix elements are evaluated. The group--subgroup in question is that of the…
Matrix generators for the general and special linear groups, the symplectic groups and the general and special unitary groups over finite fields. For the most part the generators have been obtained by translating Steinberg's generators for…
Explicit forms are given of matrix elements of generalized coherent operators based on Lie algebras su(1,1) and su(2). We also give a kind of factorization formula of the associated Laguerre polynomials.
A generating function for the Wigner's $D$-matrix elements of $SU(3)$ is derived. From this an explicit expression for the individual matrix elements is obtained in a closed form.
We derive the matrix elements of generators of unitary irreducible representations of SL(2,C) with respect to basis states arising from a decomposition into irreducible representations of SU(1,1). This is done with regard to a discrete…
The characteristic identity formalism discussed in our recent articles is further utilized to derive matrix elements of type 2 unitary irreducible $gl(m|n)$ modules. In particular, we give matrix element formulae for all gl(m|n) generators,…
A FORTRAN code for generating the leading SU(3) irreducible representation (irrep) of N identical spin 1/2 fermions in a harmonic oscillator mean field is introduced. The basis states are labeled by N--the total number of particles, the…
For the second fundamental representation of the general linear group over a commutative ring $R$ we construct straightforward and uniform polynomial expressions of elementary generators as products of elementary conjugates of an arbitrary…
Generators of the quantum $SU_q(2)$ algebra are obtained in the explicit form in the basis where the operator $\exp {J_z\over 2} J_x \exp {J_z\over 2}$ is diagonal. It is shown that the solution of this problem is related to the…
This paper introduces the concept of a generating set for stochastic matrices -- a subset of matrices whose repeated composition generates the entire set. Understanding such generating sets requires specifying the "indivisible elements" and…
A simplified boson realization of the $so_q(3)$ subalgebra of $u_q(3)$ is constructed. A simplified form of the corresponding $so_q(3)$ basis states is obtained. The reduced matrix elements of a special second-rank tensor operator…
Matrices of the irreducible representations of double crystallographic point groups O, Td, Ox{1,I} and Tdx{1,I} are derived. The characteristic polynomials (spinor bases) up to the sixth power are obtained. The method for the derivation of…
Let $A$ be a finite subset of $L^2(\mathbb{R})$ and $p,q\in\mathbb{N}$. We characterize the Schauder basis properties in $L^2(\mathbb{R})$ of the Gabor system $$G(1,p/q,A)=\{e^{2\pi i m x}g(x-np/q) : m,n\in \mathbb{Z}, g\in A\},$$ with a…
Generalised matrix elements of the irreducible representations of the quantum $SU(2)$ group are defined using certain orthonormal bases of the representation space. The generalised matrix elements are relatively infinitesimal invariant with…
The pseudo-SU(3) model is extended to explicitly include the spin and proton-neutron degrees of freedom. A general formalism for evaluating matrix elements of one-body and two-body tensor operators within this framework is presented. The…
We construct the singlet Hilbert space associated with addition of SU(3) generators. This corresponds to the solution of Gauss law in lattice QCD. The normalized basis states are explicitly constructed using Schwinger Bosons. Further, we…
The general expression for the local matrix of a quantum chain $L(\theta)$ with the site space in any representation of $su(3)$ is obtained. This is made by generalizing $L(\theta)$ from the fundamental representation and imposing the…
We generalize Sepasdar's method for finding a generator matrix of two-dimensional cyclic codes to find an independent subset of a general multicyclic code, which may form a basis of the code as a vector subspace. A generator matrix can be…