In this paper‎, ‎we have shown that the coset diagrams for the‎ ‎action of a linear-fractional group $Gamma$ generated by the linear-fractional‎ ‎transformations $r:zrightarrow frac{z-1}{z}$ and $s:zrightarrow frac{-1}{2(z+1)}$ on‎ ‎the rational projective line is connected and transitive‎. ‎By using coset diagrams‎, ‎we have shown that $r^{3}=s^{4}=1$ are defining relations for $Gamma$‎. ‎Furt...

The normal form and the coset correlation function of an arbitrary linear recurring m-array over F2 are introduced. It is proved that the normal form can be determined by its coset correlation function. Introduction Nguyen [3] studied the coset correlation of m-sequences and pointed out that the coset correlation provides an attractive technique for detecting the normal form when m-sequences ar...

It is shown that the space of cohomology classes of the SU(1, 1)/U(1) coset at negative level k contains states of relevant conformal dimensions. These states correspond to the energy density operator of the associated nonlinear sigma model. We exhibit that there exists a subclass of relevant operators forming a closed fusion algebra. We make use of these operators to perform renormalizable per...

We explain how one can construct a class of discrete hypergroups which are non-unimodular. They arise as double coset hypergroups induced by the transitive action of a non-unimodular group of permutations on an innnite set. A concrete example is given in terms of the aane group of a homogeneous tree.

The double-spinor formalism, proposed by Aisaka and Kazama, provides a basis for the pure-spinor formalism, which allows manifestly super-Poincaré covariant quantization of superstrings. We extend it to the case of backgrounds realized by coset superspaces. A general method constructing reparametrization invariant action is given by using two concrete examples, the flat space-time and AdS5 × S....