## Kyoto Journal of Mathematics

### Spin networks, Ehrhart quasipolynomials, and combinatorics of dormant indigenous bundles

Yasuhiro Wakabayashi

#### Abstract

It follows from work of S. Mochizuki, F. Liu, and B. Osserman that there is a relationship between Ehrhart’s theory concerning rational polytopes and the geometry of the moduli stack classifying dormant indigenous bundles on a proper hyperbolic curve in positive characteristic. This relationship was established by considering the (finite) cardinality of the set consisting of certain colorings on a $3$-regular graph called spin networks. In the present article, we recall the correspondences between spin networks, lattice points of rational polytopes, and dormant indigenous bundles and present some identities and explicit computations of invariants associated with the objects involved.

#### Article information

Source
Kyoto J. Math., Volume 59, Number 3 (2019), 649-684.

Dates
Revised: 5 April 2017
Accepted: 15 May 2017
First available in Project Euclid: 2 July 2019

https://projecteuclid.org/euclid.kjm/1562032985

Digital Object Identifier
doi:10.1215/21562261-2019-0020

Mathematical Reviews number (MathSciNet)
MR3990181

Zentralblatt MATH identifier
07108006

#### Citation

Wakabayashi, Yasuhiro. Spin networks, Ehrhart quasipolynomials, and combinatorics of dormant indigenous bundles. Kyoto J. Math. 59 (2019), no. 3, 649--684. doi:10.1215/21562261-2019-0020. https://projecteuclid.org/euclid.kjm/1562032985

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