This paper is a continuation of [33] at which several coset subalgebras of the lattice VOA V2E8 were constructed and the relationship between such algebras with the famous McKay observation on the extended E8 diagram and the Monster simple group were discussed. In this article, we shall provide the technical details. We completely determine the structure of the coset subalgebras constructed and...

Let G be a locally compact hypergroup and let K sub-hypergroup of G. (G, K) is Gelfand pair if Mc(G//K), the algebra measures with support on double coset G//K, commutative for convolution. In this paper, assuming that pair, we define study Fourier transform then establish Plancherel theorem K).

Let A" be a compact Hausdorff homogeneous space and G be the full group of homeomorphisms from X to X. We denote the isotropy group at x by Gx. If G is topologized by uniform convergence [l], then it is well known that G is a topological group, and the function 6: G/GX—*X, defined by 6{gGx)=g{x) is one-one and continuous. It is an open problem whether ô is a homeomorphism, i.e., whether X is a ...

We prove that for every homogeneous and strongly locally homogeneous Polish space X there is a Polish group admitting a transitive action on X. We also construct an example of a homogeneous Polish space which is not a coset space and on which no separable metrizable topological group acts transitively.

graham higman has defined coset diagrams for psl(2,ℤ). these diagrams are composed of fragments, and the fragments are further composed of two or more circuits. q. mushtaq has proved in 1983 that existence of a certain fragment γ of a coset diagram in a coset diagram is a polynomial f in ℤ[z]. higman has conjectured that, the polynomials related to the fragments are monic and for a fixed degree...

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} = {(...