CaltechAUTHORS
Published November 1, 2012 | Version public
Journal Article Metadata-only

Twisted Elliptic Genus for K3 and Borcherds Product

Creators

  • 1. ROR icon Kyoto University
  • 2. ROR icon California Institute of Technology
  • 3. ROR icon Kyushu University

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.

Additional Information

© 2012 Springer. Received: 28 December 2011; Revised: 28 April 2012; Accepted: 8 May 2012 Published online: 26 May 2012. T.E. would like thank California Institute for Technology and Professors H. Ooguri and J.H. Schwarz for Moore distinguished scholarship during the fall of 2011 and kind hospitality. K.H. thanks the Simons Center for Geometry and Physics for hospitality in the summer of 2011. The authors would like to thank H. Aoki for sending them an unpublished manuscript. Thanks are also to M. Kaneko for communications. This work is supported in part by Grant-in-Aid from the Ministry of Education, Culture, Sports, Science and Technology of Japan.

Additional details

Identifiers

Eprint ID
35642
DOI
10.1007/s11005-012-0569-2
Resolver ID
CaltechAUTHORS:20121126-134444344

Related works

Describes
10.1007/s11005-012-0569-2 (DOI)

Funding

Ministry of Education, Culture, Sports, Science and Technology of Japan Grant-in-Aid

Dates

Created
2012-11-27
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Updated
2021-11-09
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