TY - JOUR
TI - Cominuscule flag varieties and their quantum K-theory
DO - https://doi.org/doi:10.7282/T3K35XH6
PY - 2017
AB - This thesis investigates the ring structure of the torus-equivariant quantum K-theory ring QKT(X) for a cominuscule flag variety X. As a main result, we present an identity that relates the product of opposite Schubert classes in QKT(X) to the minimal degree of a rational curve joining the corresponding Schubert varieties. Using this we infer further properties of the ring QKT(X), one of which is that the Schubert structure constants always sum to one. We also introduce a formula for the quantum product of Schubert classes in projective space Pn. As a corollary we establish Griffeth-Ram positivity of the Schubert structure constants for QKT(Pn). After a closer analysis, we conclude that the rings QKT(Pn) are isomorphic for all n.
KW - Mathematics
LA - eng
ER -