Ian Marshall (Moscow): Poisson reduction on the space of polygons

Friday 23 Mar 2012, 14:00 → 15:00 Europe/Budapest

Tanacsterem

Abstract : A Poisson structure is defined on the space $\text{Undefined control sequence cW}$ of twisted polygons in $\text{Undefined control sequence RR}$. Poisson reductions with respect to two Poisson group actions on $\text{Undefined control sequence cW}$ are described. 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. In general, for any $\nu$, reduction gives rise to a family of bihamiltonian structures on the reduced space.