Euler characteristics in the quantum K-theory of flag varieties

• Anders S. Buch ^[1] ; Sjuvon Chung ^[2] ; Changzheng Li ^[3] ; Leonardo C. Mihalcea ^[4]
  1. [1] Rutgers University

     Rutgers University

     City of New Brunswick, Estados Unidos

     
  2. [2] Ohio State University

     Ohio State University

     City of Columbus, Estados Unidos

     
  3. [3] Sun Yat-sen University

     Sun Yat-sen University

     China

     
  4. [4] Virginia Tech, USA

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• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 26, Nº. 2, 2020
• Idioma: inglés
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• Resumen

  • We prove that the sheaf Euler characteristic of the product of a Schubert class and an opposite Schubert class in the quantum K-theory ring of a (generalized) flag variety G/P is equal to qd, where d is the smallest degree of a rational curve joining the two Schubert varieties. This implies that the sum of the structure constants of any product of Schubert classes is equal to 1. Along the way, we provide a description of the smallest degree d in terms of its projections to flag varieties defined by maximal parabolic subgroups.