The SO(5)⊃ SO(3) spherical harmonics form a natural basis for expansion of nuclear collective model angular wave functions. They underlie the recently-proposed algebraic method for diagonalization of the nuclear collective model Hamiltonian in an SU(1, 1)× SO(5) basis. We present a computer code for explicit construction of the SO(5)⊃ SO(3) spherical harmonics and use them to compute the Clebsc...

I USE the term covariants to include invariants, and I write particularly concerning lists of covariants (groundforms) of the binary quintic and sextic, those of quantics of lower degree being few and well known. When the weight of a covariant is spoken of in this article, it must be understood to mean the weight of its first term or "source." The symbol 5ft will denote that covariant of the qu...

We characterize the angular polyspectra, of arbitrary order, associated with isotropic fields defined on the sphere S = { (x, y, z) : x + y + z = 1 } . Our techniques rely heavily on group representation theory, and specifically on the properties of Wigner matrices and Clebsch-Gordan coefficients. The findings of the present paper constitute a basis upon which one can build formal procedures fo...

GLh(n) × GLh′(m)-covariant (hh)-bosonic (or (hh)-fermionic) algebras Ahh′±(n,m) are built in terms of the corresponding Rh and Rh′-matrices by contracting the GLq(n) × GLq±1(m)-covariant q-bosonic (or q-fermionic) algebras A q± (n,m), α = 1, 2. When using a basis of A q± (n,m) wherein the annihilation operators are contragredient to the creation ones, this contraction procedure can be carried o...

Many non-Abelian finite subgroups of SU(3) have been used to explain the flavor structure of the Standard Model. In order to systematize and classify successful models, a detailed knowledge of their mathematical structure is necessary. In this paper we shall therefore look closely at the series of finite non-Abelian groups known as ∆(6n), its smallest members being S3 (n = 1) and S4 (n = 2). Fo...

We relate the canonical basis of the Fock space representation of the quantum affine algebra Uq(ĝln), as defined by Leclerc and Thibon [LT], to the canonical basis of its restriction to Uq(sln), regarded as a based module in the sense of Lusztig. More generally we consider the restriction to any Levi subalgebra. We deduce results on decomposition numbers and branching coefficients of Schur alge...

Abstract Tailoring constituent layers can lead to improved mechanical properties of layered metals. In this work, we designed and fabricated two samples Al. One sample with AA3003 AA1060 the other only layers. The effects these designs on deformation behaviors are revealed by in-situ monitoring local strain evolution. It was found that larger microstructural textural variations a difference in ...

In [AO] the authors study Steiner bundles via their unstable hyperplanes and proved that (see [AO], Tmm 5.9) : A rank n Steiner bundle on Pn which is SL(2,C) invariant is a Schwarzenberger bundle. In this note we give a very short proof of this result based on Clebsch-Gordon problem for SL(2,C)modules.

We analyse a supersymmetric string-inspired model of all fermion masses and mixing angles based on the Pati-Salam SU(4)×SU(2)L×SU(2)R gauge group supplemented by a U(1)X flavour symmetry. The model involves third family Yukawa unification and predicts the top mass and the ratio of the vacuum expectation values tanβ. The model also provides a successful description of the CKM matrix and predicts...