Representation Theory of Three-dimensional Corner Symmetries
Abstract
We study the representation theory of the three-dimensional extended corner symmetry group associated with a circular corner. Using induced representation techniques, we construct families of representations of the infinite-dimensional corner symmetry group and analyze their unitarity and irreducibility. We also determine the maximal central extension of the symmetry group and construct the corresponding projective representations. The analysis is motivated by the role that corner symmetries play in quantum gravity, where boundary degrees of freedom --- acted upon by the corner transformations --- are expected to encode aspects of the quantum structure of spacetime. In three dimensions, the representation-theoretic structures that emerge are closely related to symmetry groups and quantum theories that already appeared as central to the study of gravity. This work provides a first step toward a systematic description of quantum gravitational corner degrees of freedom in three dimensions.
Related
- Local conservation laws and symmetries of three-dimensional incompressible Euler flow
- Webs and finite dimensional representation theory for quantum symmetric pairs
- Longitudinal electric corner modes in continuum quantum gauge theory with matter
- Corner Regularity and Asymptotics for the Two-Dimensional Radiation Transport Equation
- Sophus Lie's problem on two-dimensional metrics with projective symmetries: completing the local classification
BibTeX
@misc{neri2026representation,
title = {{Representation Theory of Three-dimensional Corner Symmetries}},
author = {Giulio Neri and Ludovic Varrin},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.17666},
eprint = {2609.17666},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.17666},
}
RIS
TY - UNPB
TI - Representation Theory of Three-dimensional Corner Symmetries
AU - Giulio Neri
AU - Ludovic Varrin
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.17666
UR - https://arxiv.org/abs/2609.17666
AB - We study the representation theory of the three-dimensional extended corner symmetry group associated with a circular corner. Using induced representation techniques, we construct families of representations of the infinite-dimensional corner symmetry group and analyze their unitarity and irreducibility. We also determine the maximal central extension of the symmetry group and construct the corresponding projective representations. The analysis is motivated by the role that corner symmetries play in quantum gravity, where boundary degrees of freedom --- acted upon by the corner transformations --- are expected to encode aspects of the quantum structure of spacetime. In three dimensions, the representation-theoretic structures that emerge are closely related to symmetry groups and quantum theories that already appeared as central to the study of gravity. This work provides a first step toward a systematic description of quantum gravitational corner degrees of freedom in three dimensions.
ER -