We give efficient quantum algorithms for HIDDEN TRANSLATION and HIDDEN SUBGROUP in a large class of non-abelian groups including solvable groups of bounded exponent and of bounded derived series. Our algorithms are recursive. For the base case, we solve efficiently HIDDEN TRANSLATION in Z p , whenever p is a fixed prime. For the induction step, we introduce the problem ORBIT COSET generalizing ...

Fusion rules for Wess-Zumino-Witten (WZW) models at fractional level can be defined in two ways, with distinct results. The Verlinde formula yields fusion coefficients that can be negative. These signs cancel in coset fusion rules, however. On the other hand, the fusion coefficients calculated from decoupling of singular vectors are non-negative. They produce incorrect coset fusion rules, howev...

Some mathematical questions relating to Coset Conformal field theories (CFT) are considered in the framework of Algebraic Quantum Field Theory as developed previously by us. We consider the issue of fix point resolution in the diagonal coset of type A. We show how to decompose certain reducible representations into irreducibles, and prove that the coset CFT gives rise to a unitary Modular Tenso...

The concept of the ‘Wigner rotation’, familiar from the composition law of (pure) Lorentz transformations, is described in the general setting of Lie group coset spaces and the properties of coset representatives. Examples of Abelian and non-Abelian Wigner rotations are given. The Lorentz group Wigner rotation, occurring in the coset space SL(2, R)/SO(2) SO(2, 1)/SO(2), is shown to be an analyt...

In this paper various methods for computing the support weight enumerators of binary, linear, even, isodual codes are described. It is shown that there exist relationships between support weight enumerators and coset weight distributions of a code that can be used to compute partial information about one set of these code invariants from the other. The support weight enumerators and complete co...