and the Monster simple group was discussed. In this paper, we will provide the technical details. We will determine the structure of the coset subalgebras and show that they are all generated by two conformal vectors of central charge 1/2.We also study the representation theory of these coset subalgebras and show that the product of two Miyamoto involutions is in the desired conjugacy class of ...

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...

We study the double cosets of a Lie group by a compact Lie subgroup. We show that a Weil formula holds for double coset Lie hypergroups and show that certain representations of the Lie group lift to representations of the double coset Lie hypergroup. We characterize smooth (analytic) vectors of these lifted representations.

Distinguished involutions in the affine Weyl groups, defined by G. Lusztig, play an essential role in the Kazhdan-Lusztig combinatorics of these groups. A distinguished involution is called canonical if it is the shortest element in its double coset with respect to the finite Weyl group. Each two-sided cell in the affine Weyl group contains precisely one canonical distinguished involution. In t...

The triple factorization of a group $G$ has been studied recently showing that $G=ABA$ for some proper subgroups $A$ and $B$ of $G$, the definition of rank-two geometry and rank-two coset geometry which is closely related to the triple factorization was defined and calculated for abelian groups. In this paper we study two infinite classes of non-abelian finite groups $D_{2n}$ and $PSL(2,2^{n})$...

We study two group theoretic problems, Group Intersection and Double Coset Membership, in the setting of black-box groups, where Double Coset Membership generalizes a set of problems, including Group Membership, Group Factorization, and Coset Intersection. No polynomial-time classical algorithms are known for these problems. We show that for solvable groups, there exist efficient quantum algori...

Coset enumeration, based on the methods described by Todd & Coxeter, is one of the basic tools for investigating nitely presented groups. The process is not well understood, and various pathological presentations of, for example, the trivial group have been suggested as challenge problems. Here we consider one such presentation. We show that it is much easier than it rst appears, albeit at the ...

This article presents the examination of the possibility that group Eg' F21 operates on a symmetric design with parameters (133,33,8) as its automorphism group. The method based on coset enumeration in group is used.

We construct smallest known trivalent graphs for girths 16 and 18. One construction uses voltage graphs, and the other coset enumeration techniques for group presentations. AMS Subject Classifications: 05C25, 05C35

After explicitly constructing the symmetric space sigma model lagrangian in terms of the coset scalars of the solvable Lie algebra gauge in the current formalism we derive the field equations of the theory.