A <i>q</i>-Analogue of the Higher Order Painlevé Type Equations with the Affine Weyl Group Symmetry of Type <i>D</i>

• Masuda Tetsu

  Aoyama Gakuin University

Bibliographic Information

Other Title

• A <i>q</i>-Analogue of the Higher Order Painlev&eacute; Type Equations with the Affine Weyl Group Symmetry of Type <i>D</i>
• A $q$-analogue of the higher order Painlevé type equations with the affine Weyl group symmetry of type $D$.

Abstract

We present a q-difference analogue of the higher order differential equations of Painlevé type whose symmetry can be described by the affine Weyl group of type D, so-called the Sasano system. It is derived from the birational realization of Weyl groups as a group of pseudo isomorphisms of certain algebraic varieties. The continuous limit is also investigated.

Journal

• Funkcialaj Ekvacioj

  Funkcialaj Ekvacioj 58 (3), 405-430, 2015

  Division of Functional Equations, The Mathematical Society of Japan

Keywords

• Cremona transformation
• <i>q</i>-difference equation
• Painlevé equation
• Rational variety
• Tropical representation
• Weyl group
• Continuous limit
• Sasano system

Details

• CRID: 1390001205112893952
• NII Article ID: 130005117041
• DOI: 10.1619/fesi.58.405
• ISSN: 05328721
• Web Site: https://www.jstage.jst.go.jp/article/fesi/58/3/58_405/_pdf
• Text Lang: en
• Data Source:
  • JaLC
  • Crossref
  • CiNii Articles
• Abstract License Flag: Disallowed