We relate the mechanism of matter creation in the universe after inflation to a simple and universal mathematical property of extended N > 1 supergravities and related compactifications of superstring theory. We show that in all such models, the inflaton field may decay into vector fields due to a nonminimal scalar-vector coupling. This coupling is compulsory for all scalars except N = 2 hypers...

We study realizations of the exceptional non-linear (quadratically generated, or W type) N = 8 and N = 7 superconformal algebras with Spin(7) and G2 affine symmetry currents, respectively. Both the N = 8 and N = 7 algebras admit unitary highestweight representations in terms of a single boson and free fermions in 8 of Spin(7) and 7 of G2, with the central charges c8 = 26/5 and c7 = 5, respectiv...

It is shown that the coset lattice of a finite group has shellable order complex if and only if the group is complemented. Furthermore, the coset lattice is shown to have a Cohen–Macaulay order complex in exactly the same conditions. The group theoretical tools used are relatively elementary, and avoid the classification of finite simple groups and of minimal finite simple groups. © 2006 Elsevi...

There is much interest in finding short presentations for the finite simple groups. In a previous paper we produced nice efficient presentations for all small simple groups and for their covering groups. Here we extend those results from simple group order less than 100,000 up to order one million, but we leave one simple group and one covering group for which the efficiency question remains un...

Recently an action formulation, called the general WZW orbifold action, was given for each sector of every WZW orbifold. In this paper we gauge this action by general twisted gauge groups to find the action formulation of each sector of every coset orbifold. Connection with the known current-algebraic formulation of coset orbifolds is discussed as needed, and some large examples are worked out ...

We lift the bosonic AdS4 × CP 3 solution of type IIA supergravity preserving 24 supersymmetries to a D = 10 superspace which has 32 Grassmann–odd directions. The type IIA superspace is obtained from D = 11 via dimensional reduction of the coset superspace OSp(8|4)/SO(7) × SO(1, 3) by realizing the latter as a Hopf fibration over the former. This construction generalizes to superspace the Hopf f...

There are q+q right PGL2(Fq)−cosets in the group PGL2(Fq2). In this paper, we present a method of generating all the coset representatives, which runs in time Õ(q), thus achieves the optimal time complexity up to a constant factor. Our algorithm has applications in solving discrete logarithms and finding primitive elements in finite fields of small characteristic.

We develop a systematic method to construct the boundary states in the coset conformal field theory G/H . Based on the relation of the G/H theory with the tensor product theory G×H , we give a map from the boundary states of G×H to those of G/H . Our map provides a large class of boundary states in coset theories, which include those not factorizable into the G and the H sectors. The action of ...

The Todd-Coxeter algorithm described in [13] remains a primary reference for coset enumeration programs. It may be viewed as a means of constructing permutation representations of finitely presented groups. A number of effective computer programs for singlecoset enumeration have been described, see, for example, [2, 7, 8]. Enumerating double cosets, rather than single cosets, gives substantial ...

Akl, S., G. Laborite, M. Leeder and K. Qiu, On doing Todd-Coxeter coset enumeration in parallel, Discrete Applied Mathematics 34 (1991) 27-35. The Todd-Coxeter coset enumeration method is without any doubt the best known and most used method in computational group theory. Surprisingly, however, it seems that no attempt has yet been made at producing a parallel version of it. This paper reports ...