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Torus Orbits On Homogeneous Varieties And Kac Polynomials Of Quivers, Paul Gunnells, Emmanuel Letellier, Fernando Rodriguez Villegas
Torus Orbits On Homogeneous Varieties And Kac Polynomials Of Quivers, Paul Gunnells, Emmanuel Letellier, Fernando Rodriguez Villegas
Paul Gunnells
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.
On The Cohomology Of Linear Groups Over Imaginary Quadratic Fields, Herbert Gangl, Paul Gunnells, Jonathan Hanke, Achill Schurmann, Mathieu Dutour Sikiric, Dan Yasaki
On The Cohomology Of Linear Groups Over Imaginary Quadratic Fields, Herbert Gangl, Paul Gunnells, Jonathan Hanke, Achill Schurmann, Mathieu Dutour Sikiric, Dan Yasaki
Paul Gunnells
Let be the group GLN(OD), where OD is the ring of integers in the imaginary quadratic field with discriminant D < 0. In this paper we investigate the cohomology of for N = 3, 4 and for a selection of discriminants: D −24 when N = 3, and D = −3,−4 when N = 4. In particular we compute the integral cohomology of up to p-power torsion for small primes p. Our main tool is the polyhedral reduction theory for developed by Ash [4, Ch. II] and Koecher [18]. Our results extend work of Staffeldt [29], who treated the case n = 3, D = −4. In a sequel [11] to this paper, we will apply some of these results to the computations with the K-groups K4(OD), when D = −3,−4.