Monodromy of the equivariant quantum differential equation of the cotangent bundle of a Grassmannian

• Vitaly Tarasov ^[2] ; Alexander Varchenko ^[1]
  1. [1] Purdue University

     Purdue University

     Township of Wabash, Estados Unidos

     
  2. [2] Department of Mathematics, University of North Carolina, USA
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 30, Nº. 2, 2024, págs. 1-33
• Idioma: inglés
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• Resumen

  • We describe the monodromy of the equivariant quantum differential equation of the cotangent bundle of a Grassmannian in terms of the equivariant K-theory algebra of the cotangent bundle. This description is based on the hypergeometric integral representations for solutions of the equivariant quantum differential equation. We identify the space of solutions with the space of the equivariant K-theory algebra of the cotangent bundle. In particular, we show that for any element of the monodromy group, all entries of its matrix in the standard basis of the equivariant K-theory algebra of the cotangent bundle are Laurent polynomials with integer coefficients in the exponentiated equivariant parameters.