• Corpus ID: 231698863

Characteristic equation for symplectic groupoid and cluster algebras

  title={Characteristic equation for symplectic groupoid and cluster algebras},
  author={Leonid Olegovich Chekhov and Michael Shapiro and Huang Shibo},
. We use the Darboux coordinate representation found by two of the authors (L.Ch. and M.Sh.) for entries of general symplectic leaves of the A n -groupoid of upper-triangular matrices to express roots of the characteristic equation det( A − λ A T ) = 0, with A ∈ A n , in terms of Casimirs of this Darboux coordinate representation, which is based on cluster variables of Fock–Goncharov higher Teichm¨uller spaces for the algebra sl n . We show that roots of the characteristic equation are simple… 
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