Euler characteristic of stable envelopes

• Hunter Dinkins ^[1] ; Andrey Smirnov ^[1]
  1. [1] University of North Carolina at Chapel Hill

     University of North Carolina at Chapel Hill

     Township of Chapel Hill, Estados Unidos

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 28, Nº. 4, 2022
• Idioma: inglés
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• Resumen

  • In this paper we prove a formula relating the equivariant Euler characteristic of Ktheoretic stable envelopes to an object known as the index vertex for the cotangent bundle of the full flag variety. Our formula demonstrates that the index vertex is the power series expansion of a rational function. This result is a consequence of the 3d mirror self-symmetry of the variety considered here. In general, one expects an analogous result to hold for any two varieties related by 3d mirror symmetry.