2012/06/15 by Li, Changzheng, Mihalcea, Leonardo C. · 1 citation
#14M15 #14N15 (Secondary) #14N35 (Primary) 19E08 #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1206.3593
Let X=G/P be a homogeneous space and ek be the class of a simple coroot in H2(X). A theorem of Strickland shows that for almost all X, the variety of pointed lines of degree ek, denoted Zk(X), is again a homogeneous space. For these X we show that the 3-point, genus 0, equivariant K-theoretic Gromov-Witten invariants of lines of degree ek are equal to quantities obtained in the (ordinary) equivariant K-theory of Zk(X). We apply this to compute the structure constants Nu,vw, ek for degree ek from the multiplication of two Schubert classes in the equivariant quantum K-theory ring of X. Using geometry of spaces of lines through Schubert or Richardson varieties we prove vanishing and positivity properties of Nu,vw,ek. This generalizes many results about K-theory and quantum cohomology of X, and also gives new identities among the structure constants in equivariant K-theory of X.