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Equivariant K-theory of quaternionic flag manifolds

Published online by Cambridge University Press:  27 November 2009

Augustin-Liviu Mare  and
Matthieu Willems
Augustin-Liviu Mare
Affiliation:
Department of Mathematics and Statistics, University of Regina, College West 307.14, Regina, Saskatchewan, S4S 0A2, Canada, [email protected]
Matthieu Willems
Affiliation:
Department of Mathematics, McGill University, 805 Sherbrooke Street West, Montréal, Québec, H3A 2K6, Canada, [email protected]
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Abstract

We consider the manifold Fln(ℍ) = Sp(n)/Sp(1)n of all complete flags in ℍn, 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 = (S1)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 KT(Fln(ℍ)) as a subring of KT(Sp(n)/T). This ring is well known, since Sp(n)/T is a complex flag variety.

Keywords

equivariant topological K-theoryquaternionic flag manifoldcomplex flag manifoldsGoresky-Kottwitz-MacPherson type presentation
Type
Research Article
Information
Journal of K-Theory , Volume 4 , Issue 3 , December 2009 , pp. 537 - 557
Copyright
Copyright © ISOPP 2009

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