On the Liouville Integrability of the Periodic Kostant–Toda Flow on Matrix Loops of Level k

Luen Chau Li, Zhaohu Nie

Research output: Contribution to journalArticle

Abstract

In this work, we consider the periodic Kostant–Toda flow on matrix loops in sl(n, C) of level k, which correspond to periodic infinite band matrices with period n with lower bandwidth equal to k and fixed upper bandwidth equal to 1 with 1’s on the first superdiagonal. We show that the coadjoint orbits through the submanifold of such matrix loops can be identified with those of a finite-dimensional Lie group, which appears in the form of a semi-direct product. We then characterize the generic coadjoint orbits and obtain an explicit global cross-section for such orbits. We also establish the Liouville integrability of the periodic Kostant–Toda flow on such orbits via the construction of action-angle variables.

Original languageEnglish (US)
Pages (from-to)1153-1203
Number of pages51
JournalCommunications In Mathematical Physics
Volume352
Issue number3
DOIs
StatePublished - Jun 1 2017

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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