Equivariant K-theory of quaternionic flag manifolds

摘要

We consider the manifold FIn(H) = Sp(n)/Sp(1)(n) of all complete flags in H-n, where H is the skew-field of quaternions. We study its equivariant complex K-theory rings with respect to the action of two groups: Sp(1)(n) and a certain canonical subgroup T = (S-l)(n) (a maximal torus). For the first group action we obtain a Goresky-Kottwitz-MacPherson type description. For the second one, we describe the ring K-T(FIn (H)) as a subring of K-T (Sp(n)/T). This ring is well known, since Sp(n)/T is a complex flag variety.