Duke Mathematical Journal

A gerbe for the elliptic gamma function

Giovanni Felder, André Henriques, Carlo A. Rossi, and Chenchang Zhu

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Abstract

The identities for elliptic gamma functions discovered by Felder and Varchenko [8] 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

Article information

Source
Duke Math. J., Volume 141, Number 1 (2008), 1-74.

Dates
First available in Project Euclid: 4 December 2007

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1196794290

Digital Object Identifier
doi:10.1215/S0012-7094-08-14111-0

Mathematical Reviews number (MathSciNet)
MR2372147

Zentralblatt MATH identifier
1130.33010

Subjects
Primary: 33E30: Other functions coming from differential, difference and integral equations
Secondary: 20L05: Groupoids (i.e. small categories in which all morphisms are isomorphisms) {For sets with a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H05} 57S25: Groups acting on specific manifolds

Citation

Felder, Giovanni; Henriques, André; Rossi, Carlo A.; Zhu, Chenchang. A gerbe for the elliptic gamma function. Duke Math. J. 141 (2008), no. 1, 1--74. doi:10.1215/S0012-7094-08-14111-0. https://projecteuclid.org/euclid.dmj/1196794290


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