We study a coset-space unification model for families based on E 7 /SU(5)×U(1) 3. We find that qualitative structure of quark and lep-ton mass matrices in this model describes very well the observation. We stress, in particular, that the large mixing angle, sin 2 2θ νµντ ≃ 1, required for the atmospheric neutrino oscillation reported by the Su-perKamiokande collaboration, is naturally obtained,...

We review the recently discovered connection between the Belinsky-Khalatnikov-Lifshitz-like “chaotic” structure of generic cosmological singularities in eleven-dimensional supergravity and the “last” hyperbolic Kac-Moody algebra E10. This intriguing connection suggests the existence of a hidden “correspondence” between supergravity (or even M-theory) and null geodesic motion on the infinite-dim...

Several interesting features of coset models " without fixed points " are easily understood via Chern-Simons theory. In this paper we derive explicit formulae for the handle-squashing operator in these cosets. These operators are fixed, linear combinations of the irreducible representations of the coset. As a simple application of these curious formulae, we compute the traces of all genus-one o...

We derive the Green-Schwarz action on AdS 5 × S 5 using an alternate version of the coset superspace construction. By Wick rotations and Lie algebra identifications we bring the coset to GL(4|4)/(Sp(4) ⊗ GL(1)) 2 , which allows us to represent the conformal transformations on unconstrained matrices. The derivation is more streamlined even for the bosonic sector, and conformal symmetry is manife...

In this paper new infinite families of linear binary completely transitive codes are presented. They have covering radius ρ = 3 and 4, and are a half part of the binary Hamming and the binary extended Hamming code of length n = 2 − 1 and 2, respectively, where m is even. From these new completely transitive codes, in the usual way, i.e., as coset graphs, new presentations of infinite families o...

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 ...

A general Lagrangian formulation of integrably deformed G/H-coset models is given. We consider the G/H-coset model in terms of the gauged Wess-Zumino-Witten action and obtain an integrable deformation by adding a potential energy term Tr(gTgT̄ ), where algebra elements T, T̄ belong to the center of the algebra h associated with the subgroup H. We show that the classical equation of motion of the ...

‎there is much interest in finding short presentations for the finite‎ ‎simple groups‎. ‎indeed it has been suggested that all these groups are‎ ‎efficient in a technical sense‎. ‎in previous papers we produced nice‎ ‎efficient presentations for all except one of the simple groups with‎ ‎order less than one million‎. ‎here we show that all simple groups with‎ ‎order between $1$ million and $5$ ...

The mathematical framework for an exact quantization of the two-dimensional coset space σmodels coupled to dilaton gravity, that arise from dimensional reduction of gravity and supergravity theories, is presented. This work extends the previous results of [45]. The two-time Hamiltonian formulation is obtained, which describes the complete phase space of the model in the whole isomonodromic sect...

We give efficient quantum algorithms for the problems of Hidden Translation and Hidden Subgroup in a large class of non-abelian solvable groups including solvable groups of constant exponent and of constant length derived series. Our algorithms are recursive. For the base case, we solve efficiently Hidden Translation in Zp , whenever p is a fixed prime. For the induction step, we introduce the ...