The coset and double-coset decompositions of the 420 subgroups of m(z)3(xyz)m(xy)1' (O(h)1') and the 236 subgroups of 6(z)/m(z)m(x)m(1)1' (D(6h)1') with respect to each of their subgroups are calculated along with additional mathematical properties of these groups.

Abstract Let G be a finite group. $H, K$ subgroups of and $H \backslash / the double coset space. If Q is probability on which constant conjugacy classes ( $Q(s^{-1} t s) = Q(t)$ ), then random walk driven by projects to Markov chain /K$ . This allows analysis lumped using representation theory Examples include coagulation-fragmentation processes natural chains contingency tables. Our main exam...

We investigate a class of reducible yet indecomposable modules over the N=2 superconformal algebras. These so-called staggered exhibit non-diagonalisable action Virasoro mode L0. Using recent results on coset construction minimal models, we explicitly construct such for central charges c=−1 and c=−6. also describe spectral-flow orbits symmetries families which arise via coset.

The concept of a coset-preserving skew-morphism is a generalization of the widely studied t-balanced skew-morphisms of regular Cayley maps which are in turn generalizations of group automorphisms. In case of abelian groups, all skew-morphisms of regular Cayley maps are roots of coset-preserving skew-morphisms, and therefore, classification of cosetpreserving skew-morphisms of finite abelian gro...

Conformal field theories with ŝl(2)−1/2 symmetry are studied with a view to investigating logarithmic structures. Applying the parafermionic coset construction to the non-logarithmic theory, a part of the structure of the triplet model is uncovered. In particular, the coset theory is shown to admit the triplet W -algebra as a chiral algebra. This motivates the introduction of an augmented ŝl(2)...

Let A be a local commutative principal ideal ring. We study the double coset space of GLn(A) with respect to the subgroup of upper triangular matrices. Geometrically, these cosets describe the relative position of two full flags of free primitive submodules of A. We introduce some invariants of the double cosets. If k is the length of the ring, we determine for which of the pairs (n, k) the dou...

We extend the analysis [18] of the canonical structure of the Wess-Zumino-Witten theory to the bulk and boundary coset G/H models. The phase spaces of the coset theories in the closed and in the open geometry appear to coincide with those of a double ChernSimons theory on two different 3-manifolds. In particular, we obtain an explicit description of the canonical structure of the boundary G/G c...

We study states of large charge density in integrable conformal coset models. For the O(2) coset, we consider two different S-matrices, one corresponding to a Thirring mass perturbation and the other to the continuation to O(2+ ). The former leads to simplification in the conformal limit; the latter gives a more complicated description of the O(2) system, with a large zero mode sector in additi...

A simple sphere bound gives the best possible tradeoff between the volume per point of an infinite array and its error probability on an additive white Gaussian noise (AWGN) channel. It is shown that the sphere bound can be approached by a large class of coset codes or multilevel coset codes with multistage decoding, including certain binary lattices. These codes have structure of the kind that...