Equivariant $K$-theory of quaternionic flag manifolds

Details Equivariant $K$-theory of quaternionic flag manifolds Equivariant $K$-theory of quaternionic flag manifolds

2007-10-19

arxiv.org/abs/0710.3766v3

Mathematics

Algebraic Topology

Final version: 18 pages

Scientific paper

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

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