K-theory of weight varieties

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2 Citations (Scopus)


Let T be a compact torus and (M,ω) a Hamiltonian Tspace. We give a new proof of the K-theoretic analogue of the Kirwan surjectivity theorem in symplectic geometry (see Harada-Landweber, 2007) by using the equivariant version of the Kirwan map introduced in Goldin, 2002. We compute the kernel of this equivariant Kirwan map, and hence give a computation of the kernel of the Kirwan map. As an application, we find the presentation of the kernel of the Kirwan map for the T-equivariant K-theory of flag varieties G/T where G is a compact, connected and simply-connected Lie group. In the last section, we find explicit formulae for the K-theory of weight varieties.

Original languageEnglish
Pages (from-to)251-267
Number of pages17
JournalNew York Journal of Mathematics
Publication statusPublished - 2011
Externally publishedYes


  • Equivariant K-theory
  • Flag variety
  • Kirwan surjectivity
  • Symplectic quotient
  • Weight variety

ASJC Scopus subject areas

  • General Mathematics


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