gl3 ALGEBRA IN MIXED MATRIX REPRESENTATIONS
It is demonstrated that the so-called mixed realization of the gl3 algebra generators in terms of matrix differential operators in two variables, as presented by Smirnov-Turbiner (2013), can be “lifted” into the action in the Fock space associated with the five-dimensional Heisenberg algebra h5. A realization of the gl3 generators in terms of matrix finite-difference (translation-invariant) operators, matrix discrete (dilatation-invariant) operators, matrix complex operators in (z, z̄), and their mixtures is presented.
Authors
- Alexander V. Turbiner (ORCID: https://orcid.org/0000-0002-9415-6748)
Institutions
- Universidad Nacional Autónoma de México (MX)
Publication Details
- Journal
- Acta Polytechnica
- Published
- 2025-11-07
- DOI
- https://doi.org/10.14311/ap.2025.65.0562
- Primary Topic
- Quantum Mechanics and Non-Hermitian Physics
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Dirección General de Asuntos del Personal Académico, Universidad Nacional Autónoma de México