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.
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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@article{CRMATH_2015__353_5_415_0, author = {Freed, Daniel S. and Teleman, Constantin}, title = {Dirac families for loop groups as matrix factorizations}, journal = {Comptes Rendus. Math\'ematique}, pages = {415--419}, publisher = {Elsevier}, volume = {353}, number = {5}, year = {2015}, doi = {10.1016/j.crma.2015.02.011}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.crma.2015.02.011/} }
TY - JOUR AU - Freed, Daniel S. AU - Teleman, Constantin TI - Dirac families for loop groups as matrix factorizations JO - Comptes Rendus. Mathématique PY - 2015 SP - 415 EP - 419 VL - 353 IS - 5 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2015.02.011/ DO - 10.1016/j.crma.2015.02.011 LA - en ID - CRMATH_2015__353_5_415_0 ER -
%0 Journal Article %A Freed, Daniel S. %A Teleman, Constantin %T Dirac families for loop groups as matrix factorizations %J Comptes Rendus. Mathématique %D 2015 %P 415-419 %V 353 %N 5 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2015.02.011/ %R 10.1016/j.crma.2015.02.011 %G en %F CRMATH_2015__353_5_415_0
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://www.numdam.org/articles/10.1016/j.crma.2015.02.011/
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