Geodesic
Loop groups and twisted $K$-theory III
Daniel S. Freed1 ; Michael J. Hopkins2 ; Constantin Teleman3
1 Department of Mathematics<br/> The University of Texas at Austin<br/> Austin, TX 78712
2 Department of Mathematics<br/>Harvard University<br/>Cambridge, MA 02138
3 Department of Mathematics<br/> University of California, Berkeley<br/> Berkeley, CA 94720-3840
Annals of mathematics, Tome 174 (2011) no. 2, pp. 947-1007.

Voir la notice de l'article provenant de la source Annals of Mathematics website

In this paper, we identify the Ad-equivariant twisted $K$-theory of a compact Lie group $G$ with the “Verlinde group” of isomorphism classes of admissible representations of its loop groups. Our identification preserves natural module structures over the representation ring $R(G)$ and a natural duality pairing. Two earlier papers in the series covered foundations of twisted equivariant $K$-theory, introduced distinguished families of Dirac operators and discussed the special case of connected groups with free $\pi_1$. Here, we recall the earlier material as needed to make the paper self-contained. Going further, we discuss the relation to semi-infinite cohomology, the fusion product of conformal field theory, the rôle of energy and a topological Peter-Weyl theorem.
DOI : 10.4007/annals.2011.174.2.5

Daniel S. Freed 1 ; Michael J. Hopkins 2 ; Constantin Teleman 3

1 Department of Mathematics<br/> The University of Texas at Austin<br/> Austin, TX 78712
2 Department of Mathematics<br/>Harvard University<br/>Cambridge, MA 02138
3 Department of Mathematics<br/> University of California, Berkeley<br/> Berkeley, CA 94720-3840 
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Daniel S. Freed; Michael J. Hopkins; Constantin Teleman. Loop groups and twisted $K$-theory III. Annals of mathematics, Tome 174 (2011) no. 2, pp. 947-1007. doi : 10.4007/annals.2011.174.2.5. http://geodesic.mathdoc.fr/articles/10.4007/annals.2011.174.2.5/

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