4 problems

Turbiner's Euclidean-geometry separation conjecture
Turbiner's second conjecture. If the symbol of $H$ engenders a Euclidean geometry, then the spectral equation $H\psi=E\psi$ can be solved by separation of variables. The paper stat…
opendifferential-geometry schrodinger-operators separation-of-variables
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04
Turbiner's non-separability conjecture for flat Schrödinger operators
A quasi-exactly-solvable or exactly-solvable problem in $\mathbb{R}^2$ is one containing the Laplace–Beltrami operator with a flat-space metric tensor; its variables are non-separa…
opendifferential-geometry schrodinger-operators separation-of-variables
0 responses
05
Conjecture on self-annihilating invariance vector fields for Lie–Poisson systems
Self-annihilating invariance-vector-field conjecture. Among the invariance vector fields there exists a special vector field $Z$ which, acting in the system of natural Lie-algebrai…
openlie-poisson-geometry separation-of-variables
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03
The functional-equation characterization of the $gl_{1|2}$ transfer-matrix spectrum
Let $T_{1}^{(K)}(\lambda)$ be the transfer matrix of the general $gl_{1|2}$ -graded Yang–Baxter algebra with twisted boundary conditions. Let $t_{1}(\lambda \mid \{x_a\})$ be the po…
openintegrable-systems separation-of-variables yang-baxter-algebras
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06

Turbiner's Euclidean-geometry separation conjecture