Notes on the K3 Surface and the Mathieu Group M 24

By Tohru Eguchi, Hirosi Ooguri, Yuji Tachikawa. Experimental Mathematics, 2010

323 citations recorded by the source corpus.

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 remains a mystery.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8aa5320910a849dcfdc95d59fa70843f6719b68c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Discrete Mathematics and Combinatorics

1. S. Hohenegger
2. J. Duncan
3. R. Volpato
4. Don Zagier
5. Miranda C. N. Cheng
6. J. Harvey
7. M. Gaberdiel

In Geometry and Topology

1. J. Duncan
2. Miranda C. N. Cheng
3. M. Gaberdiel
4. S. Hohenegger
5. R. Volpato
6. J. Harvey
7. S. Murthy
8. Don Zagier

In Mathematical Physics

1. Miranda C. N. Cheng
2. J. Duncan
3. M. Gaberdiel
4. S. Hohenegger
5. R. Volpato
6. S. Murthy
7. Don Zagier
8. A. Dabholkar

Citations in the corpus

• Symmetries of K3 sigma models (2011, methodology): “They are also relevant for the analysis of ‘Mathieu Moonshine’ [1] that was reviewed at the beginning of the Introduction.”
• Quantum Black Holes, Wall Crossing, and Mock Modular Forms (2012, background): “We expect that the general framework of mock modular forms and Jacobi forms developed in this paper is likely to have varied physical applications in the context of non-compact conformal field theories, wall-crossings in enumerative geometry, and recently formulated Mathieu and umbral moonshine conj”
• Umbral Moonshine (2012, methodology): “conjecture relating the H (2) g and the group G is nothing but the conjecture relating (scalarvalued) mock modular forms and the largest Mathieu group M24 that has been investigated recently [15, 19, 24, 20, 21, 22, 108, 109].”