Asymptotics of quantum spin networks at a fixed root of unity

作者：Garoufalidis Stavros^*; van der Veen Roland

来源：Mathematische Annalen, 2012, 352(4): 987-1012.

DOI：10.1007/s00208-011-0662-3

A classical spin network consists of a ribbon graph (i.e., an abstract graph with a cyclic ordering of the vertices around each edge) and an admissible coloring of its edges by natural numbers. The standard evaluation of a spin network is an integer number. In a previous paper, we proved an existence theorem for the asymptotics of the standard evaluation of an arbitrary classical spin network when the coloring of its edges are scaled by a large natural number. In the present paper, we extend the results to the case of an evaluation of quantum spin networks of arbitrary valency at a fixed root of unity. As in the classical case, our proofs use the theory of G-functions of Andre, together with some new results concerning holonomic and q-holonomic sequences of Wilf-Zeilberger.

• 出版日期2012-4