Geodesic
Lie algebras/Topology
Dirac families for loop groups as matrix factorizations
[Familles d'opérateurs de Dirac pour les groupes de lacets et factorisations en matrices]

Présenté par : Michèle Vergne

Freed, Daniel S.1 ; Teleman, Constantin2
1 UT Austin, Mathematics Department, RLM 8.100, 2515 Speedway C1200, Austin, TX 78712, USA
2 UC Berkeley, Mathematics Department, 970 Evans Hall #3840, Berkeley, CA 94720, USA
Comptes Rendus. Mathématique, Tome 353 (2015) no. 5, pp. 415-419.

Voir la notice de l'article provenant de la source Numdam

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.

On identifie la catégorie des représentations intégrables de plus bas poids du groupe de lacets LG d'un groupe de Lie compact G avec la catégorie des complexes de Fredholm tordus, courbés et équivariants pour conjugaison sur le groupe G : plus précisément, les factorisations en matrices d'un potentiel provenant de la rotation des lacets dans LG. Cette construction relève l'isomorphisme de K-groupes de [3–5] en une équivalence de catégories. La construction fait appel aux familles d'opérateurs de Dirac.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2015.02.011

Freed, Daniel S. 1 ; Teleman, Constantin 2

1 UT Austin, Mathematics Department, RLM 8.100, 2515 Speedway C1200, Austin, TX 78712, USA
2 UC Berkeley, Mathematics Department, 970 Evans Hall #3840, Berkeley, CA 94720, USA 
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Freed, Daniel S.; Teleman, Constantin. Dirac families for loop groups as matrix factorizations. Comptes Rendus. Mathématique, Tome 353 (2015) no. 5, pp. 415-419. doi : 10.1016/j.crma.2015.02.011. http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2015.02.011/

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