On Quantum Vortex Field Equation and Exact Solutions

Using triple (G, h, k_B), I construct Quantum Vortex Field Equation (QVFE) u_t=▽u▽(D(u)▽u) extended from u_t=▽u△u.
The exact solutions describe deformations of quantum gravity.
My object is giving an automorphism representation of CFT. The Hecke algebra models intertwining operators of unramified principal series of vortex growth or contract. I explain the role of spectral triple of Boltzmann-Planck irredicible group in the QVFE. These exact analytical solutions in a complex torus S¹ or spheres Sⁿ visually and precisely describe the dynamical behaviours of vertex core and vortex filament under gravity effect, including their period and maximum deformation of mass and velocity.
L discovers some important facts on quantum vortex, as the character distribution, push-forward, pull-back and simple flip confinite endomorphisms, as on light propagation periodity and ergodity as light speed is ν_c = 2n + √3 ∈ S¹. Another an interesting fact is on vortex core spin law: α¹=½√3 + ½i; α²=½+ ½√3i; α³ = i; α⁶ = -1; α⁹ = -i; α¹²= +1 = I_d .
The key results prove that:
1. Maximum light speed is not 3x10⁸m/s;
2. All are governed by Quantum Gravity and Boltzmann - Planck dual groupoid;
3. Boltzmann variety is topological form of cusp or vertex point; Planck variety is then of circle or smooth manifolds.