The spectra of finite 3-transposition groups

TL;DR

This paper computes the spectra of diagrams associated with finite 3-transposition groups, which are relevant in the study of vertex operator algebras and Griess subalgebras.

Contribution

It provides explicit spectral calculations for diagrams of all finite 3-transposition groups, linking group theory with algebraic structures in vertex operator algebras.

Findings

Spectra computed for all finite 3-transposition groups' diagrams

Identification of minimal eigenvalues relevant to algebraic structures

Connections established between group spectra and vertex operator algebra subalgebras

Abstract

We calculate the spectrum of the diagram for each finite $3$-transposition group. Such graphs with a given minimal eigenvalue have occurred in the context of compact Griess subalgebras of vertex operator algebras.