Abstract
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.
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@article {wend, MRKEY = {2114428},
AUTHOR = {Wendt, Robert},
TITLE = {A character formula for representations of loop groups based on non-simply connected {L}ie groups},
JOURNAL = {Math. Z.},
FJOURNAL = {Mathematische Zeitschrift},
VOLUME = {247},
YEAR = {2004},
NUMBER = {3},
PAGES = {549--580},
ISSN = {0025-5874},
CODEN = {MAZEAX},
MRCLASS = {22E67 (17B67)},
MRNUMBER = {2114428},
MRREVIEWER = {Alessandro Mani{à}},
DOI = {10.1007/s00209-003-0629-5},
ZBLNUMBER = {1063.22022},
}
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