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A general Chevalley formula for semi-infinite flag manifolds and quantum K-theory.
- Source :
-
Selecta Mathematica, New Series . Jul2024, Vol. 30 Issue 3, p1-44. 44p. - Publication Year :
- 2024
-
Abstract
- We give a Chevalley formula for an arbitrary weight for the torus-equivariant K-group of semi-infinite flag manifolds, which is expressed in terms of the quantum alcove model. As an application, we prove the Chevalley formula for an anti-dominant fundamental weight for the (small) torus-equivariant quantum K-theory Q K T (G / B) of a (finite-dimensional) flag manifold G/B; this has been a longstanding conjecture about the multiplicative structure of Q K T (G / B) . In type A n - 1 , we prove that the so-called quantum Grothendieck polynomials indeed represent (opposite) Schubert classes in the (non-equivariant) quantum K-theory Q K (S L n / B) ; we also obtain very explicit information about the coefficients in the respective Chevalley formula. [ABSTRACT FROM AUTHOR]
- Subjects :
- *POLYNOMIALS
*QUANTUM graph theory
Subjects
Details
- Language :
- English
- ISSN :
- 10221824
- Volume :
- 30
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Selecta Mathematica, New Series
- Publication Type :
- Academic Journal
- Accession number :
- 176781379
- Full Text :
- https://doi.org/10.1007/s00029-024-00924-8