Published in Journal of Gökova Geometry Topology, Volume 10 (2016)
Title Naturality of FHT isomorphism
Author Doman Takata
Freed, Hopkins and Teleman constructed an isomorphism (we call it FHT isomorphism) between twisted equivariant K-theory of compact Lie group and the "Verlinde ring" of the loop group of ([FHT1, FHT2, FHT3]). However, naturality of the isomorphism with respect to group homomorphisms has not been verified. We construct induced homomorphisms and for whose tangent map is injective. is a positive central extension of the loop group of , so that FHT isomorphism is a natural transformation between two objects. In fact, we construct another object char and verify that three objects are naturally isomorphic with respect to , and we introduce. Moreover, we extend these constructions for K-theory and to compact connected Lie group with torsion-free and homomorphism satisfying the "decomposable condition", and verify that they are isomorphic. This is a generalization of naturality of verified in [FHT1].
Keywords Loop groups, twisted equivariant K-theory, representation theory
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Submitted: Aug 3, 2015
Accepted: July 8, 2016
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