Letters in Mathematical Physics

, Volume 102, Issue 2, pp 203–222 | Cite as

Twisted Elliptic Genus for K3 and Borcherds Product

  • Tohru Eguchi
  • Kazuhiro HikamiEmail author


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.

Mathematics Subject Classification

58J26 81T40 20C34 14J28 


elliptic genus superconformal algebra moonshine Mathieu group Jacobi form mock theta function 


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Copyright information

© Springer 2012

Authors and Affiliations

  1. 1.Yukawa Institute for Theoretical PhysicsKyoto UniversityKyotoJapan
  2. 2.California Institute of TechnologyPasadenaUSA
  3. 3.Faculty of MathematicsKyushu UniversityFukuokaJapan

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