Residues formulas for the push-forward in K-theory, the case of G2/P

Abstract

We study residue formulas for push-forward in K-theory of homogeneous spaces. First we review formulas for classical groups, which we derive from a formula for the classical Grassmannian case. Next we consider the homogeneous spaces for G2. One of them embeds in the Grassmannian Gr(2,7). We find its fundamental class in the equivariant K-theory and obtain the residue formula for the push-forward. This formula is valid for G2/B as well.