Equivariant K-theory of quaternionic flag manifolds

2007/10/19 by Augustin-Liviu Mare, Mare, Augustin-Liviu, Matthieu Willems +1 · 1 citation
Mathematics · #14M17 #19L47 #55N15 #57N65 #Advanced Combinatorial Mathematics #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric and Algebraic Topology #math.AT #msc:14M17 #msc:19L47 #msc:55N15 #msc:57N65

paper · pdf · doi:10.48550/arxiv.0710.3766

Final version: 18 pages

openalex publication_date 2007/10/19 · arxiv created 2009/07/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

Citations

• Homogeneous vector bundles on homogeneous spaces

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