### Abstract

We discuss the relation between the elliptic genus of K3 surface and the Mathieu group M _{24}. We find that some of the twisted elliptic genera for K3 surface, defined for conjugacy classes of the Mathieu group M _{24}, can be represented in a very simple manner in terms of the η product of the corresponding conjugacy classes. It is shown that our formula is a consequence of the identity between the Borcherds product and additive lift of some Siegel modular forms.

Original language | English |
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Pages (from-to) | 203-222 |

Number of pages | 20 |

Journal | Letters in Mathematical Physics |

Volume | 102 |

Issue number | 2 |

DOIs | |

Publication status | Published - Nov 1 2012 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Letters in Mathematical Physics*,

*102*(2), 203-222. https://doi.org/10.1007/s11005-012-0569-2

**Twisted Elliptic Genus for K3 and Borcherds Product.** / Eguchi, Tohru; Hikami, Kazuhiro.

Research output: Contribution to journal › Article

*Letters in Mathematical Physics*, vol. 102, no. 2, pp. 203-222. https://doi.org/10.1007/s11005-012-0569-2

}

TY - JOUR

T1 - Twisted Elliptic Genus for K3 and Borcherds Product

AU - Eguchi, Tohru

AU - Hikami, Kazuhiro

PY - 2012/11/1

Y1 - 2012/11/1

N2 - We discuss the relation between the elliptic genus of K3 surface and the Mathieu group M 24. We find that some of the twisted elliptic genera for K3 surface, defined for conjugacy classes of the Mathieu group M 24, can be represented in a very simple manner in terms of the η product of the corresponding conjugacy classes. It is shown that our formula is a consequence of the identity between the Borcherds product and additive lift of some Siegel modular forms.

AB - We discuss the relation between the elliptic genus of K3 surface and the Mathieu group M 24. We find that some of the twisted elliptic genera for K3 surface, defined for conjugacy classes of the Mathieu group M 24, can be represented in a very simple manner in terms of the η product of the corresponding conjugacy classes. It is shown that our formula is a consequence of the identity between the Borcherds product and additive lift of some Siegel modular forms.

UR - http://www.scopus.com/inward/record.url?scp=84867714038&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84867714038&partnerID=8YFLogxK

U2 - 10.1007/s11005-012-0569-2

DO - 10.1007/s11005-012-0569-2

M3 - Article

AN - SCOPUS:84867714038

VL - 102

SP - 203

EP - 222

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

SN - 0377-9017

IS - 2

ER -