2015/02/12 by Doman Takata, Takata, Doman
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1502.03761
openalex publication_date 2015/02/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Freed, Hopkins and Teleman constructed an isomorphism between twisted equivariant K-theory of compact Lie group G and the "Verlinde ring" of the loop group of G. We call this isomorphism FHT isomorphism. However, it does not hold naturality with respect to group homomorphisms. We construct two "quasi functors" t.e.K (a modification of twisted equivariant K-theory) and RL (a modification of representation group of loop groups) so that FHT isomorphism is natural transformation between two "quasi functors" for tori, that is, we construct two "induced homomorphisms" of the "quasi functors" t.e.K and RL for a group homomorphism whose tangent map is injective between two tori. In fact, we construct another quasi functor char and verify that three quasi functors are naturally isomorphic. Moreover, we extend the quasi functor t.e.K and char to compact connected Lie group with torsion-free fundamental group and group homomorphism satisfying "the decomposable condition", and verify that they are isomorphic. This is a generalization of a result in [FHT1].