Equivariant K-theory of GKM bundles

Given a fiber bundle of GKM spaces, pi: M -> B, we analyze the structure of the equivariant K-ring of M as a module over the equivariant K-ring of B by translating the fiber bundle, pi, into a fiber bundle of GKM graphs and constructing, by combinatorial techniques, a basis of this module consisting of K-classes which are invariant under the natural holonomy action on the K-ring of M of the fundamental group of the GKM graph of B. We also discuss the implications of this result for fiber bundles pi: M -> B where M and B are generalized partial flag varieties and show how our GKM description of the equivariant K-ring of a homogeneous GKM space is related to the Kostant-Kumar description of this ring.


Published in:
Annals Of Global Analysis And Geometry, 43, 1, 31-45
Year:
2013
Publisher:
Dordrecht, Springer
ISSN:
0232-704X
Keywords:
Laboratories:




 Record created 2013-03-28, last modified 2018-03-17


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