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Open Access Publications from the University of California

Dirac families for loop groups as matrix factorizations

  • Author(s): Freed, DS
  • Teleman, C
  • et al.

© 2015 Académie des sciences. We identify the category of integrable lowest-weight representations of the loop group LG of a compact Lie group G with the category of twisted, conjugation-equivariant curved Fredholm complexes on the group G: namely, the twisted, equivariant matrix factorizations of a super-potential built from the loop rotation action on LG. This lifts the isomorphism of K-groups of [3-5] to an equivalence of categories. The construction uses families of Dirac operators.

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