Peter Crooks

activity

20132023

most citedAbstract integrable systems on hyperkähler manifolds arising from Slodowy slices

5 citations · 17 across the 20 of their papers we have counts for

collaborators

23 papers

math.AG2023★ 1 cited

Universal families of twisted cotangent bundles

Peter Crooks

Given a complex algebraic group $G$ and complex $G$ -variety $X$ , one can study the affine Hamiltonian Lagrangian (AHL) $G$ -bundles over $X$ . Lisiecki indexes the isomorphism classe…

math.SG2023

The double Gelfand-Cetlin system, invariance of polarization, and the Peter-Weyl theorem

Peter Crooks, Jonathan Weitsman

The bundle map $T^{*} U (n) ⟶ U (n)$ provides a real polarization of the cotangent bundle $T^{*} U (n)$ , a…

math.SG2023

Abelianization and the Duistermaat-Heckman theorem

Peter Crooks, Jonathan Weitsman

Fix a compact connected Lie group $G$ with Lie algebra $g$ , as well as a strong Gelfand-Cetlin datum on $g^{*}$ . Let us also fix a connected symplectic manifold…

math.SG2022★ 1 cited

Gelfand-Cetlin abelianizations of symplectic quotients

Peter Crooks, Jonathan Weitsman

We show that generic symplectic quotients of a Hamiltonian $G$ -space $M$ by the action of a compact connected Lie group $G$ are also symplectic quotients of the same manifold $M$ b…

math.SG2021

Symplectic reduction along a submanifold

Peter Crooks, Maxence Mayrand

We introduce the process of symplectic reduction along a submanifold as a uniform approach to taking quotients in symplectic geometry. This construction holds in the categories of…

math.SG2021

On the singularities of Mishchenko-Fomenko systems

Peter Crooks, Markus Röser

To each complex semisimple Lie algebra $g$ and regular element $a \in g_{reg}$ , one associates a Mishchenko-Fomenko subalgebra $\mathcal{F}_a\subseteq\ma…