Poisson geometry of the Grothendieck resolution of a complex semisimple group

Details Poisson geometry of the Grothendieck resolution of a complex semisimple group Poisson geometry of the Grothendieck resolution of a complex semisimple group

2006-10-03

arxiv.org/abs/math/0610123v2

Mathematics

Quantum Algebra

Final version for publication in MMJ, added references

Scientific paper

We study a Poisson structure $\pi$ on the Grothendieck resolution $X$ of a complex semi-simple group $G$ and prove that the desingularization map $\mu:(X,\pi) \to (G,\pi_0)$ is Poisson, where $\pi_0$ is a Poisson structure such that intersections of conjugacy classes and opposite Bruhat cells $BwB_-$ are Poisson subvarieties. We compute the symplectic leaves of $X$ and show that $(X, \pi)$ resolves singularities of $(G, \pi_0)$.

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