1Department Mathematik, Friedrich-Alexander-Universität, Erlangen-Nürnberg, Germany 2Dipartimento di Matematica, Università di Roma Tor Vergata, Roma, Italy
Journal of Lie Theory, Tome 35 (2025) no. 4, pp. 689-718
We study the relation between representations of certain infinite-dimensional Lie groups and those of the associated conformal nets. For a chiral conformal net extending the net generated by the vacuum representation of a loop group or diffeomorphism group of the circle, we show that any conformal net representation induces a positive-energy representation of the corresponding group. Consequently, we prove that any representation of such a conformal net is automatically diffeomorphism covariant. Moreover, we show that the covariance cocycles of conformal net representations satisfy naturality with respect to the action of diffeomorphisms, i.e. the diffeomorphisms act equivariantly on the category of conformal net representations.
1
Department Mathematik, Friedrich-Alexander-Universität, Erlangen-Nürnberg, Germany
2
Dipartimento di Matematica, Università di Roma Tor Vergata, Roma, Italy
Maria Stella Adamo; Luca Giorgetti; Yoh Tanimoto. Representations of Conformal Nets Associated with Infinite-Dimensional Groups. Journal of Lie Theory, Tome 35 (2025) no. 4, pp. 689-718. http://geodesic.mathdoc.fr/item/JOLT_2025_35_4_a1/
@article{JOLT_2025_35_4_a1,
author = {Maria Stella Adamo and Luca Giorgetti and Yoh Tanimoto},
title = {Representations of {Conformal} {Nets} {Associated} with {Infinite-Dimensional} {Groups}},
journal = {Journal of Lie Theory},
pages = {689--718},
year = {2025},
volume = {35},
number = {4},
url = {http://geodesic.mathdoc.fr/item/JOLT_2025_35_4_a1/}
}
TY - JOUR
AU - Maria Stella Adamo
AU - Luca Giorgetti
AU - Yoh Tanimoto
TI - Representations of Conformal Nets Associated with Infinite-Dimensional Groups
JO - Journal of Lie Theory
PY - 2025
SP - 689
EP - 718
VL - 35
IS - 4
UR - http://geodesic.mathdoc.fr/item/JOLT_2025_35_4_a1/
ID - JOLT_2025_35_4_a1
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%J Journal of Lie Theory
%D 2025
%P 689-718
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%U http://geodesic.mathdoc.fr/item/JOLT_2025_35_4_a1/
%F JOLT_2025_35_4_a1
