Almost representations of algebras and quantization
Mathematical Physics
2022-02-01 v3 math.MP
Representation Theory
Symplectic Geometry
Abstract
We introduce the notion of almost representations of Lie algebras and quantum tori, and establish an Ulam-stability type phenomenon: every irreducible almost representation is close to a genuine irreducible representation. As an application, we prove that geometric quantizations of the two-dimensional sphere and the two-dimensional torus are conjugate in the semi-classical limit up to a small error.
Cite
@article{arxiv.2005.11693,
title = {Almost representations of algebras and quantization},
author = {Louis Ioos and David Kazhdan and Leonid Polterovich},
journal= {arXiv preprint arXiv:2005.11693},
year = {2022}
}
Comments
51 pages. Revised and corrected version