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Notes on the K3 Surface and the Mathieu group M_24

Tohru Eguchi, Hirosi Ooguri, Yuji Tachikawa

TL;DR

It is pointed out that the elliptic genus of the K3 surface has a natural decomposition in terms of dimensions of irreducible representations of the largest Mathieu group M 24.

Abstract

We point out that the elliptic genus of the K3 surface has a natural decomposition in terms of dimensions of irreducible representations of the largest Mathieu group M_24. The reason is yet a mystery.

Notes on the K3 Surface and the Mathieu group M_24

TL;DR

It is pointed out that the elliptic genus of the K3 surface has a natural decomposition in terms of dimensions of irreducible representations of the largest Mathieu group M 24.

Abstract

We point out that the elliptic genus of the K3 surface has a natural decomposition in terms of dimensions of irreducible representations of the largest Mathieu group M_24. The reason is yet a mystery.

Paper Structure

This paper contains 2 sections, 20 equations, 1 table.

Table of Contents

  1. Data of $M_{24}$
  2. $M_{24}$ and the classical geometry of K3