The double-spinor formalism, proposed by Aisaka and Kazama, provides a basis for the pure-spinor formalism, which allows manifestly super-Poincaré covariant quantization of superstrings. We extend it to the case of backgrounds realized by coset superspaces. A general method constructing reparametrization invariant action is given by using two concrete examples, the flat space-time and AdS5 × S....

We describe the couplings of six-dimensional supergravity, which contain a self-dual tensor multiplet, to n T anti-self-dual tensor matter multiplets, n V vector multiplets and n H hypermultiplets. The scalar fields of the tensor multiplets form a coset SO(nT , 1)/SO(nT ), while the scalars in the hypermultiplets form quaternionic Kähler symmetric spaces, the generic example being Sp(nH , 1)/Sp...

Let a finite presentation be given for an associative, in general non-commulative algebra E, with identity, over a field. We study an algorithm for the construction, from this presentation, of linear, i.e, matrix, representations of this algebra. A set of vector constraints which is given as part of the initial data determines which particular representation of E is produced. This construction ...

A brief overview of strings propagating on noncompact coset spaces G/H is presented in terms of gauged WZW models. The role played by isometries in the existence of target space duality and by fixed points of the gauged transformations in the existence of singularities and horizons, is emphasized. A general classification of the spaces with a single time-like coordinate is presented. The spacet...

We perform the non-linear realisation or the coset formulation of the pure N = 4, D = 5 supergravity. We derive the Lie superalgebra which parameterizes a coset map whose induced Cartan-Maurer form produces the bosonic field equations of the pure N = 4, D = 5 supergravity by canonically satisfying the Cartan-Maurer equation. We also obtain the first-order field equations of the theory as a twis...

Julius Whiston showed that the size of an independent generating set in the symmetric group Sn is at most n−1. We determine all sets meeting this bound. We also give some general remarks on the maximum size of an independent generating set of a group and its relationship to coset geometries for the group. In particular, we determine all coset geometries of maximum rank for the symmetric group S...

Coset enumeration, based on the methods described by Todd and Coxeter, is one of the basic tools for investigating nitely presented groups. The process is not well understood, and various pathological presentations of, for example, the trivial group have been suggested as challenge problems. Here we consider one such family of presentations proposed by B.H. Neumann. We show that the problems ar...