New relations and identities for generalized hypergeometric coefficients

AbstractGeneralized hypergeometric coefficients 〈pFq(a; b)¦λ〉 enter into the problem of constructing matrix elements of tensor operators in the unitary groups and are the expansion coefficients of a multivariable symmetric function generalization pFq(a; b; z), z = (z1, z2,…, zt), of the Gauss hypergeometric function in terms of the Schur functions eλ(z), where λ = (λ1, λ2,…, λt) is an arbitrary partition. As befits their group-theoretic origin, identities for these generalized hypergeometric coefficients characteristically involve series summed over the Littlewood-Richardson numbers g(μνλ). Identities that may be interpreted as generalizations of the Bailey, Saalschütz,… identities are developed in this paper. Of particular interest is an identity which develops in a natural way a group-theoretically defined expansion over new inhomogeneous symmetric functions. While the relations obtained here are essential for the development of the properties of tensor operators, they are also of interest from the viewpoint of special functions

Dirac Operators on Quantum Projective Spaces

We construct a family of self-adjoint operators D_N which have compact resolvent and bounded commutators with the coordinate algebra of the quantum projective space CP_q(l), for any l>1 and 0<q<1. They provide 0^+ dimensional equivariant even spectral triples. If l is odd and N=(l+1)/2, the spectral triple is real with KO-dimension 2l mod 8.Comment: 54 pages, no figures, dcpic, pdflate

Complete Labeling of G 2-Representations. Trace Formulae for Racah Operators

A trace formula is given that simultaneously allows to obtain the Casimir operators of G 2 and the (Racah) labeling operators for generic irreducible representations. The labeling operators are shown to arise as traces operators induced by a matrix decomposition. The eigenvalue problem is analyzed for the fundamental representations of G 2

Complete Labeling of G 2-Representations. Trace Formulae for Racah Operators

A trace formula is given that simultaneously allows to obtain the Casimir operators of G 2 and the (Racah) labeling operators for generic irreducible representations. The labeling operators are shown to arise as traces operators induced by a matrix decomposition. The eigenvalue problem is analyzed for the fundamental representations of G 2

What's new with the neutron and proton

The existence and importance of the proton radius puzzle, observed via a Lamb shift measurement in muonic atoms, is discussed. Possible resolutions of the puzzle are discussed. Then the broader question of the meaning of the proton radius is addressed and examples of correctly defined charge densities are presented.Gerald A. Miller, Anthony W. Thomas, Jonathan D. Carroll, Johann Rafelsk