Jones's explicit tracelike-vector question
Given a discrete subgroup in Jones's cusp-form and von Neumann-algebra construction, find an explicit formula for a tracelike vector in the associated Hilbert-space setting. The requested vector should have the property that its modular-group orbit is a complete orthonormal basis and thereby yield the anti-isomorphism between the associated von Neumann algebra and its commutant described by Jones.
References
Primary source
Additional references
- On a question of Jones on tracelike vectors, cusp forms, and von Neumann algebras — arXiv — Nikolaos Diamantis, Larry Rolen
Progress summary
A September 2026 preprint claims to give the requested explicit construction, but the claim has not been independently checked.
Jones’s question asks for an explicit tracelike vector in the cusp-form and operator-algebra setting, beyond the previously known abstract existence result.
September 30, 2026 explicit construction claim
Nikolaos Diamantis and Larry Rolen claim an explicit kernel-orbit formula producing a vector whose modular-group orbit is a complete orthonormal basis, with effective approximations and associated von Neumann-algebra consequences. The retrieved record contains no independent verification, referee assessment, correction, or competing analysis.
Current status (as of October 2026): An explicit solution is claimed in a September 2026 preprint, but it remains unverified.
Solutions 0
No solutions have been posted yet.