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 journalArticlepeer-review

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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