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
Mostrar afiliaciones +
Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 26, Nº. 2, 2020
Idioma: inglés
DOI: 10.1007/s00029-020-00557-7
Enlaces
- Texto completo
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.