Coset enumeration is one of the basic tools for investigating nitely presented groups. Many enumerations require signiicant resources, in terms of CPU time or memory space. We develop a fully functional parallel coset enumeration procedure and we discuss some of the issues involved in such parallelisation using the POSIX threads library. Our results can equally well be applied to any master-sla...

Todd and Coxeter's method for enumerating cosets of nitely generated subgroups in nitely presented groups (abbreviated by Tc here) is one famous method from combinatorial group theory for studying the subgroup problem. Since preex string rewriting is also an appropriate method to study this problem, preex string rewriting methods have been compared to Tc. We recall and compare two of them briee...

A brief overview of dimensional reductions for diffeomorphism invariant theories is given. The distinction between the physical idea of compactification and the mathematical problem of a consistent truncation is discussed, and the typical ingredients of the latter –reduction of spacetime dimensions and the introduction of constraints– are examined. The consistency in the case of of group manifo...

1 The Setup {s:setup} The starting point is: a group G, a Cartan involution θ, and another involution σ of finite order, commuting with θ. It is natural to consider the coset σK = {σ ◦ int(k) | k ∈ K} ⊂ Aut(G). Every element of this coset commutes with θ. We’re mainly interested when σ is an involution, especially the case σ = θ. Now fix a pinning P = (H,B, {Xα}), and write δ, ǫ ∈ Aut(G) for th...

We discuss a large class of coset constructions of the N=2 sl(n|n− 1) affine superalgebra. We select admissible subalgebras, i.e. subalgebras that induce linear chiral/antichiral constraints on the coset supercurrents. We show that all the corresponding coset constructions lead to N=2 matrix GNLS hierarchies. We develop an algorithm to compute the relative Hamiltonians and flows. We spell out c...

The crystalline spinon basis for the RSOS models associated with ŝl2 is studied. This basis gives fermionic type character formulas for the branching coefficients of the coset (ŝl2)l × (ŝl2)N/(ŝl2)l+N . In addition the path description of the parafermion characters is found as a limit of the spinon description of the string functions.

are considered in this paper. Examples of finite Qn-geometries are constructed for any n i> 2. In particular, we obtain new examples of finite 2-arc-transitive graphs of girth 5, containing Petersen subgraphs (cf. [4], [5] for an enquiry into this class of graphs). Furthermore, we give a complete classification of Q2-geometries using coset enumeration. In particular, we show that they are all f...

The general non-split scalar coset of supergravity theories is discussed.The symmetric space sigma model is studied in two equivalent formulations and for different coset parametrizations.The dualisation and the local first order formulation is performed for the non-split scalar coset G/K when the rigid symmetry group G is a real form of a non-compact semisimple Lie group (not necessarily split...

We analyze the hypermultiplet moduli space describing the universal sector of type IIA theory compactified on a Calabi-Yau threefold. The classical moduli space is described in terms of the coset SU(2, 1)/U(2). The flux quantization condition of the antisymmetric tensor field of M-theory implies discrete identifications for the scalar fields describing this four-dimensional quaternionic geometr...