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 ...

We discuss a new type of unitary perturbations around conformal theories inspired by the σ-model perturbation of the nonunitary WZNW model. We show that the nonunitary level k WZNW model perturbed by its sigma model term goes to the unitary level −k WZNW model. When plugged into the gauged WZNW model the given perturbation results in the perturbed gauged WZNW model which no longer describes a c...

Higman has defined coset diagrams for PGL(2, ℤ). The coset diagrams are composed of fragments, and the fragments are further composed of two or more circuits. A condition for the existence of a certain fragment γ in a coset diagram is a polynomial f in ℤ[𝔃], obtained by choosing a pair of words F[w i , w j ] such that both w i and w j fix a vertex v in γ. Two pairs of words are equivalent if an...

Example 1.1 (Cosets in R). Consider the vector space X = R. Let M be any onedimensional subspace of R, i.e., M is a line in R through the origin. A coset of M is a rigid translate of M by a vector in R. For concreteness, let us consider the case where M is the x1-axis in R , i.e., M = {(x1, 0) : x1 ∈ R}. Then given a vector y = (y1, y2) ∈ R , the coset y +M is the set y +M = {y +m : m ∈ M} = {(...

In this paper infinite families of linear binary nested completely regular codes are constructed. They have covering radius ρ equal to 3 or 4, and are 1/2-th parts, for i ∈ {1, . . . , u} of binary (respectively, extended binary) Hamming codes of length n = 2 − 1 (respectively, 2), where m = 2u. In the usual way, i.e., as coset graphs, infinite families of embedded distance-regular coset graphs...

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...