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In this paper we present a new compact expression of the elliptic genus of SL(2)/U(1)-supercoset theory by making use of the `spectral flow method' of the path-integral evaluation. This new expression is written in a form like a Poincare…

We present an analysis of the Dirac equation when the spin symmetry is changed from SU(2) to the quaternion group, $Q_8$, achieved by multiplying one of the gamma matrices by the imaginary number, $i$. The reason for doing this is to…

By using complex quaternion, which is the system of quaternion representation extended to complex numbers, we show that the laws of electromagnetism can be expressed much more simply and concisely. We also derive the quaternion…

The general theoretical ground for the models based on the compact angle coordinates is presented. It is observed that the proper dependence on compact coordinates has to be through the group elements and is achieved most naturally in a…

We know that any element A of the group SO(3) can be represented as A = A1 A2 A1', where A1, A1' are elements of SO1(2)={A is an element of SO(3) | Ae1=e1}, and SO2(2)={A is an element of SO(3) | Ae2=e2} . This fact is known as Euler's…

We give criteria for real, complex and quaternionic representations to define s-representations, focusing on exceptional Lie algebras defined by spin representations. As applications, we obtain the classification of complex representations…

We classify all compact simply connected biquotients of the form $G/\!\!/ SU(2)^2$ for $G =SU(4), SO(7), Spin(7)$, or $G = \mathbf{G}_2\times SU(2)$. In particular, we show there are precisely $2$ inhomogeneous reduced biquotients in the…

In this paper we will outline elements of the global calculus of seudo-differential operators on the group SU(2). This is a part of a more general approach to pseudo-differential operators on compact Lie groups that will appear in the…

The linear canonical transformations of geometric optics on two-dimensional screens form the group $Sp(4,R)$, whose maximal compact subgroup is the Fourier group $U(2)_F$; this includes isotropic and anisotropic Fourier transforms, screen…

Representations of the $s\ell_q(2)$ algebra are constructed in the space of polynomials of real (complex) variable for $q^N=1$. The spin addition rule based on eigenvalues of Casimir operator is illustrated on few simplest cases and…

We propose a general formulation of simplicial lattice gauge theory inspired by the finite element method. Numerical tests of convergence towards continuum results are performed for several SU(2) gauge fields. Additionaly, we perform…

Using the entropic inequalities for Shannon and Tsallis entropies new inequalities for some classical polynomials are obtained. To this end, an invertible mapping for the irreducible unitary representation of groups $SU(2)$ and $SU(1,1)$…

We demonstrate that the matrix quantum group $SL_q(2)$ gives rise to nontrivial matrix product operator representations of the Lie group $SL(2)$, providing an explicit characterization of the nontrivial global $SU(2)$ symmetry of the XXZ…

The general structure of the representation theory of a $Z_2$-graded coalgebra is discussed. The result contains the structure of Fourier analysis on compact supergroups and quantisations thereof as a special case. The general linear…

We classify all subgroups of $SO(3)$ that are generated by two elements, each a rotation of finite order, about axes separated by an angle that is a rational multiple of $\pi$. In all cases we give a presentation of the subgroup. In most…

In this paper, starting from pure group-theoretical point of view, we develop a regular approach to describing particles with different spins in the framework of a theory of scalar fields on the Poincare group. Such fields can be considered…

We give an analog of Frobenius' theorem about the factorization of the group determinant on the group algebra of finite abelian groups and we extend it into dihedral groups and generalized quaternion groups. Furthermore, we describe the…

We show that, for SU(2) generators of arbitrary dimension $D$, there exist identities that express the completely symmetric product of $D$ matrices in terms of completely symmetric products of fewer number of matrices. We also indicate why…

We consider solutions of the 2x2 matrix Hamiltonians of the physical systems within the context of the su(2) and su(1,1) Lie algebra. Our technique is relatively simple when compared with the others and treats those Hamiltonians which can…

The evaluation of a relativistic spin network for the classical case of the Lie group SU(2) is given by an integral formula over copies of SU(2). For the graph determined by a 4-simplex this gives the evaluation as an integral over a space…