The pentagram map was introduced by R. Schwartz in 1992 and is now one of the most renowned discrete integrable systems. In the present paper we show that this map, as well as all its known integrable multidimensional generalizations, can be seen as refactorization-type mappings in Poisson-Lie groups. This, in particular, provides invariant Poisson structures and a Lax form with spectral parameter for multidimensional pentagram maps. Furthermore, in an appendix, joint with B. Khesin, we introduce and prove integrability of long-diagonal pentagram maps, encompassing all known integrable cases, as well as describe their continuous limit as the Boussinesq hierarchy.
|Original language||English (US)|
|State||Published - Mar 2 2018|
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