Poisson Reduction of the Space of Polygons

DOI10.1093/IMRN/RNR252zbMATH Open1343.37077arXiv1007.1952OpenAlexW2053310847MaRDI QIDQ3196602

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Publication date: 29 October 2015

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Abstract: A family of Poisson structures, parametrised by an arbitrary odd periodic function $phi$, is defined on the space $cW$ of twisted polygons in $R{R}^u$. Poisson reductions with respect to two Poisson group actions on $cW$ are described. The $u=2$ and $u=3$ cases are discussed in detail and the general $u$ case in less detail. Amongst the Poisson structures arising in examples are to be found the lattice Virasoro structure, the second Toda lattice structure and some extended Toda lattice structures. A general result is proved showing that, for any $u$, to certain concrete choices of $phi$ there correspond compatible Poisson structures which generate all the extended bigraded Toda hierarchies of a suitable size.

Full work available at URL: https://arxiv.org/abs/1007.1952

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