ALMOST REPRESENTATIONS OF ALGEBRAS AND QUANTIZATION

Louis Ioos, David Kazhdan, Leonid Polterovich

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)1587-1629
Number of pages43
JournalAmerican Journal of Mathematics
Volume145
Issue number5
DOIs
StatePublished - Oct 2023

Funding

FundersFunder number
European Research Council757585
Israel Science Foundation1102/20

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