2012/10/02 by Koji Hasegawa
Mathematics · Physics and Astronomy · #Affine transformation #Algebraic structures and combinatorial models #Complex system #Discretization #Formalism (music) #Lax pair #Monodromy #Nonlinear Waves and Solitons #Quantization (signal processing) #Quantum Mechanics and Non-Hermitian Physics #Symmetry group #Weyl group #math-ph #math.MP #math.QA #nlin.SI
paper · pdf · doi:10.1007/s11005-013-0620-y
14 pages with 4 figures
arxiv created 2012/10/02 · openalex publication_date 2013/03/20 · arxiv updated 2015/06/11 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
A discretization of Painlevé VI equation was obtained by Jimbo and Sakai in 1996. There are two ways to quantize it: 1) use the affine Weyl group symmetry (of D5(1)) (Hasegawa, 2011), 2) Lax formalism i.e. monodromy preserving point of view. It turns out that the second approach is also successful and gives the same quantization as in the first approach.