On the “monster” simple group

Complex hyperbolic geometry and the monster simple group (conjectural)

I explained the ideas and coincidences which led me to conjecture in [2] that a group closely related to the monster simple group is got from the orbifold fundamental group of a certain 13-dimensional complex-analytic variety by adjoining a certain relation. Conway conjectured [6] that a group he called the bimonster is generated by 16 involutions satisfying certain braid and commutation relati...

On the action of the sporadic simple Baby Monster group on its conjugacy class 2B

We determine the character table of the endomorphism ring of the permutation module associated with the multiplicity-free action of the sporadic simple Baby Monster group B on its conjugacy class 2B, where the centraliser of a 2B-element is a maximal subgroup of shape 2.Co2. This is one of the first applications of a new general computational technique to enumerate big orbits. Mathematics Subje...

On the Minimal Parabolic System Related to the Monster Simple Group

Almost all of the 26 sporadic finite simple groups possess systems of subgroups which, in several ways, resemble the parabolic systems of the finite simple groups of Lie type. Many of these systems are catalogued in [RSt, RSm]. Those in [RSt] mirror more closely the minimal parabolic systems of a finite simple group of Lie type. In this paper the term minimal parabolic system will be used in a ...

Vertex Operator Algebras, Extended E8 Diagram, and Mckay’s Observation on the Monster Simple Group

We study McKay’s observation on the Monster simple group, which relates the 2A-involutions of the Monster simple group to the extended E8 diagram, using the theory of vertex operator algebras (VOAs). We first consider the sublattices L of the E8 lattice obtained by removing one node from the extended E8 diagram at each time. We then construct a certain coset (or commutant) subalgebra U associat...

The Fake Monster Formal Group