2006/01/13 by Giovanni Felder, André Henriques, Andre Henriques +2
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #math.CV #math.QA #msc:20L05 #msc:33E30 #msc:57S25
paper · pdf · doi:10.1215/s0012-7094-08-14111-0
published as Duke Math. J. 141(2008), 1-74 · 54 pages
arxiv created 2006/01/13 · openalex publication_date 2007/12/04 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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