The vector k-constrained KP hierarchy and Sato's Grassmannian

1996/08/30 by Johan van de Leur
Engineering · Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #Optical Network Technologies #math.QA #q-alg

paper · pdf · doi:10.1016/s0393-0440(97)81154-0

15 pages, AMSTeX

arxiv created 1996/08/30 · openalex publication_date 1997/08/01 · arxiv updated 2009/11/30 · openalex created_date 2020/11/23 · openalex updated_date 2026/08/01

Abstract

We use the representation theory of the infinite matrix group to show that (in the polynomial case) the n--vector k--constrained KP hierarchy has a natural geometrical interpretation on Sato's infinite Grassmannian. This description generalizes the the k--reduced KP or Gelfand--Dickey hierarchies.

Citations

• On a generalization of the Fay-Sato identity for KP Baker functions and its application to constrained hierarchies
• Solitons and Infinite Dimensional Lie Algebras