Torus orbits on homogeneous varieties and Kac polynomials of quivers
Representation Theory
2013-09-04 v1 Algebraic Geometry
Abstract
In this paper we prove that the counting polynomials of certain torus orbits in products of partial flag varieties coincides with the Kac polynomials of supernova quivers, which arise in the study of the moduli spaces of certain irregular meromorphic connections on trivial bundles over the projective line. We also prove that these polynomials can be expressed as a specialization of Tutte polynomials of certain graphs providing a combinatorial proof of the non-negativity of their coefficients.
Keywords
Cite
@article{arxiv.1309.0545,
title = {Torus orbits on homogeneous varieties and Kac polynomials of quivers},
author = {Paul E. Gunnells and Emmanuel Letellier and Fernando Rodriguez Villegas},
journal= {arXiv preprint arXiv:1309.0545},
year = {2013}
}