Integrable systems from the classical reflection equation

Gus Schrader*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We construct integrable Hamiltonian systems on G/K, where G is a coboundary Poisson-Lie group and K is a Lie subgroup arising as the fixed point set of a group automorphism σ of G satisfying the classical reflection equation. We show that the time evolution of these systems is described by a Lax equation, and under a factorizability assumption, present its solution in terms of a factorization problem in G. Our construction is closely related to the semiclassical limit of Sklyanin's integrable quantum spin chains with reflecting boundaries.

Original languageEnglish (US)
Pages (from-to)1-23
Number of pages23
JournalInternational Mathematics Research Notices
Volume2016
Issue number1
DOIs
StatePublished - 2016
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)

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