We prove a conjecture about mininmal index of certain representations of Coset Algebraic Conformal Field Theories under certain conditions as formulated previously by us. As a by-product, the Kac-Wakimoto Conjecture (KWC) which is related to the asympotics of the coset characters is true under the same conditions. The same idea in the proof also proves a recent conjecture related to subfactors ...

We show that several problems that figure prominently in quantum computing, including Hidden Coset, Hidden Shift, and Orbit Coset, are equivalent or reducible to Hidden Subgroup. We also show that, over permutation groups, the decision version and search version of Hidden Subgroup are polynomial-time equivalent. For Hidden Subgroup over dihedral groups, such an equivalence can be obtained if th...

Hamidoune’s connectivity results [11] for hierarchical Cayley digraphs are extended to Cayley coset digraphs and thus to arbitrary vertex transitive digraphs. It is shown that if a Cayley coset digraph can be hierarchically decomposed in a certain way, then it is optimally vertex connected. The results are obtained by extending the methods used in [11]. They are used to show that cycle-prefix g...

We have applied the method of dualisation to construct the coset realisation of the bosonic sector of the N = 2, D = 6 supergravity which is coupled to a tensor multiplet. The bosonic field equations are regained through the Cartan-Maurer equation which the Cartan form satisfies. The first-order formulation of the theory is also obtained as a twisted self-duality condition within the non-linear...