New York Journal of Mathematics
Volume 17 (2011) 251-267


Ho-Hon Leung

K-theory of weight varieties

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Published: March 17, 2011
Keywords: Kirwan surjectivity, flag variety, weight variety, equivariant K-theory, symplectic quotient
Subject: 53D20; 14M15, 19L47

Let T be a compact torus and (M,ω) a Hamiltonian T-space. 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.

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Department of Mathematics, Malott Hall, Cornell University, Ithaca, New York 14853-4201 USA