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Torus orbits on homogeneous varieties and Kac polynomials of quivers

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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 new way to compute them. We also discuss connections with the Gel’fand–MacPherson correspondence.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA, 01003, USA

    Paul E. Gunnells

  2. IMJ-PRG/CNRS UMR 75 86, Université Paris-Diderot, Site Sophie Germain, 75013, Paris, France

    Emmanuel Letellier

  3. Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151, Trieste, Italy

    Fernando Rodriguez Villegas

Authors
  1. Paul E. Gunnells
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  2. Emmanuel Letellier
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  3. Fernando Rodriguez Villegas
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Corresponding author

Correspondence to Emmanuel Letellier.

Additional information

Paul E. Gunnells is supported by the NSF Grant DMS-1101640. Emmanuel Letellier is supported by the Grant ANR-09-JCJC-0102-01 and ANR-13-BS01-0001-01. Fernando Rodriguez Villegas is supported by the NSF Grant DMS-1101484 and a Research Scholarship from the Clay Mathematical Institute.

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Gunnells, P.E., Letellier, E. & Villegas, F.R. Torus orbits on homogeneous varieties and Kac polynomials of quivers. Math. Z. 290, 445–467 (2018). https://doi.org/10.1007/s00209-017-2025-6

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  • DOI: https://doi.org/10.1007/s00209-017-2025-6

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