English

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.

Keywords

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

R2 v1 2026-06-23T15:46:00.228Z