Related papers: Resolution of SU(3) Outer Multiplicity Problem and…
The group SU(3) is parameterized in terms of generalized ``Euler angles''. The differential operators of SU(3) corresponding to the Lie Algebra elements are obtained, the invariant forms are found, the group invariant volume element is…
A general classification of linear differential and finite-difference operators possessing a finite-dimensional invariant subspace with a polynomial basis (the generalized Bochner problem) is given. The main result is that any operator with…
We present an explicit expression for the topological invariants associated to $SU(2)$ monopoles in the fundamental representation on spin four-manifolds. The computation of these invariants is based on the analysis of their corresponding…
Concerning the new boson representation presented in Part I, it is proved that this representation obeys the su(2)-algebra in a certain subspace in the whole boson space constructed by the Schwinger boson representation of the…
It is a well known result that the number of irreducible representations of SU(N) on a tensor product containing k factors of a vector space V is given by the number of involutions in the symmetric group on k letters. In this paper, we…
A summary of the properties of the Wigner Clebsch-Gordan coefficients and isoscalar factors for the group SU3 in the SU2$\otimes$U1 decomposition is presented. The outer degeneracy problem is discussed in detail with a proof of a conjecture…
We construct a new SO(3)$\times$SO(3) invariant non-supersymmetric solution of the bosonic field equations of $D=11$ supergravity from the corresponding stationary point of maximal gauged $N=8$ supergravity by making use of the non-linear…
The mass operator M is introduced as an independent dynamical variable which is taken as the translation generator P_4 of the inhomogenous De Sitter group. The classification of representations of the algebra P(1,4) of this group is…
We study the decomposition as an $\textrm{SO}(3)$-module of the multiplicity space corresponding to the branching from $\textrm{SO}(n+3)$ to $\textrm{SO}(n)$. Here, $\textrm{SO}(n)$ (resp.\ $\textrm{SO}(3)$) is considered embedded in…
We propose a general algorithm to compute all the symmetry classes of any $\mathrm{SO}(3)$ or $\mathrm{O}(3)$ linear representation. This method relies on the introduction of a binary operator between sets of conjugacy classes of closed…
In this paper, to solve the invariant subspace problem, contraction operators are classified into three classes ; (Case 1) completely non-unitary contractions with a non-trivial algebraic element, (Case 2) completely non-unitary…
We establish recurrences formulas of the order of the classical groups that allow us to find a generalization of Euler's angles for classical groups and the invariant measures of these groups. We find the generating function for the SU(2)…
We study Riemannian 8-manifolds with an infinitesimal action of SO(3) by which each tangent space breaks into irreducible spaces of dimensions 3 and 5. The relationship with quaternionic, almost product- and PSU-geometry is thoroughly…
We formulate a theory of invariants for the spin symmetric group in some suitable modules which involve the polynomial and exterior algebras. We solve the corresponding graded multiplicity problem in terms of specializations of the Schur…
All possible permutations in the discrete $S_4$ group are classified by three rotation angles associated with the orthogonal group $O(3)$. We construct a spinor representation ${\bf 2}_D$ of $O(3)$, which is transformed by three 4$\times$4…
We show that $\frak{su}(2)$ Lie algebras of coordinate operators related to quantum spaces with $\frak{su}(2)$ noncommutativity can be conveniently represented by $SO(3)$-covariant poly-differential involutive representations. We show that…
On the basis of the Schwinger boson representation for the Lipkin model developed in (I), the Holstein-Primakoff representation for the su(3)-algebra is presented. Including the symmetric case, the representation obtained in this paper…
Integral formulae for form factors of a large family of charged local operators in SU(2) invariant Thirring model are given extending Smirnov's construction of form factors of chargeless local operators in the sine-Gordon model. New abelian…
We propose a notion of a ternary skew-symmetric covariant tensor of 3rd order, consider it as a 3-dimensional matrix and study a ten-dimensional complex space of these tensors. We split this space into a direct sum of two five-dimensional…
The SU(3)-Casson invariant for integral homology 3-spheres as studied by Boden-Herald possesses a 'spectral flow obstruction' to being an integer valued invariant which depends only on the non-degenerate (perturbed) moduli space of flat…