Abstract
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 language | English |
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Pages (from-to) | 251-267 |
Number of pages | 17 |
Journal | New York Journal of Mathematics |
Volume | 17 |
Publication status | Published - 2011 |
Externally published | Yes |
Keywords
- Equivariant K-theory
- Flag variety
- Kirwan surjectivity
- Symplectic quotient
- Weight variety
ASJC Scopus subject areas
- General Mathematics