2004/02/17 by Hajime Nagoya, Nagoya, Hajime · 1 citation
Mathematics · Physics and Astronomy · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #math.QA
paper · pdf · doi:10.48550/arxiv.math/0402281
26 pages; v2, minor changes, corrected typos, add $l=1$ case to Section 2
openalex publication_date 2004/02/17 · arxiv created 2004/06/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose quantum Painlevé systems of type Al(1). These systems, for l=1 and l≥ 2, should be regarded as quantizations of the second Painlevé equation and the differential systems with the affine Weyl group symmetries of type Al(1) studied by M. Noumi and Y. Yamada \citeNYhigherorder, respectively. These quantizations enjoy the affine Weyl group symmetries of type Al(1) as well as the Lax representations. The quantized systems of type A1(1) and type Al(1) (l= 2n) can be obtained as the continuous limits of the discrete systems constructed from the affine Weyl group symmetries of type A2(1) and Al+1(1), respectively.