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A gerbe for the elliptic gamma function

Authors
  • Felder, Giovanni
  • Henriques, Andre
  • Rossi, Carlo A.
  • Zhu, Chenchang
Type
Published Article
Publication Date
Jan 13, 2006
Submission Date
Jan 13, 2006
Identifiers
DOI: 10.1215/S0012-7094-08-14111-0
arXiv ID: math/0601337
Source
arXiv
License
Unknown
External links

Abstract

The identities for elliptic gamma functions discovered by A. Varchenko and one of us are generalized to an infinite set of identities for elliptic gamma functions associated to pairs of planes in 3-dimensional space. The language of stacks and gerbes gives a natural framework for a systematic description of these identities and their domain of validity. A triptic curve is the quotient of the complex plane by a subgroup of rank three (it is a stack). Our identities can be summarized by saying that elliptic gamma functions form a meromorphic section of a hermitian holomorphic abelian gerbe over the universal oriented triptic curve.

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