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...

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...

Dynamical quantum groups were recently introduced by Etingof and Varchenko as an algebraic framework for studying the dynamical Yang–Baxter equation, which is precisely the Yang–Baxter equation satisfied by 6j-symbols. We investigate one of the simplest examples, generalizing the standard SU(2) quantum group. The matrix elements for its corepresentations are identified with Askey–Wilson polynom...

It is shown that the problem of reduction can be formulated in a uniform way using the theory of invariants. This provides a powerful tool of analysis and it opens the road to new applications of these algebras, beyond the context of integrable systems. Moreover, it is proven that sl2(C)–Automorphic Lie Algebras associated to the icosahedral group I, the octahedral group O, the tetrahedral grou...

I F we find it useful to distinguish short periods in the development of a science, the theory of invariants may easily enough be considered to have passed a milestone in 1887. In that year was published the second part of Gordan's Vorlesungen über Invariantentheorie. The plan of this work was dominated by the intent to expound and exemplify worthily the famous Gordan theorem on the finiteness ...

The newest progress on the study of the strangeness in the proton and in the lowest negative parity nucleon excited state N * (1535) is reviewed. Implications on the internal quark structure of the proton, N * (1535) and other baryons are discussed. The diquark cluster picture for the 5-quark components in baryons gives a natural explanation not only to the empirical indications for a positive ...

We propose an alternative for the Clebsch decomposition of currents in fluid mechanics, in terms of complex potentials taking values in a Kähler manifold. We reformulate classical relativistic fluid mechanics in terms of these complex potentials and rederive the existence of an infinite set of conserved currents. We perform a canonical analysis to find the explicit form of the algebra of conser...