4 citations · 6 across the 4 of their papers we have counts for
12 papers
Symplectic Reduction in Infinite Dimensions
Tobias Diez, Gerd Rudolph
This paper develops a theory of symplectic reduction in the infinite-dimensional setting, covering both the regular and singular case. Extending the classical work of Marsden, Wein…
Cartan Geometry and Infinite-Dimensional Kempf-Ness Theory
Tobias Diez, Akito Futaki, Tudor Ratiu
We pioneer the development of a rigorous infinite-dimensional framework for the Kempf-Ness theorem, addressing the significant challenge posed by the absence of a complexification…
Norm-squared of the momentum map in infinite dimensions with applications to Kähler geometry and symplectic connections
Tobias Diez, Tudor S. Ratiu
We initiate the study of the norm-squared of the momentum map as a rigorous tool in infinite dimensions. In particular, we calculate the Hessian at a critical point, show that it i…
Expectation values of polynomials and moments on general compact Lie groups
Tobias Diez, Lukas Miaskiwskyi
We develop a powerful framework to calculate expectation values of polynomials and moments on compact Lie groups based on elementary representation-theoretic arguments and an integ…
Normal form of equivariant maps in infinite dimensions
Tobias Diez, Gerd Rudolph
Local normal form theorems for smooth equivariant maps between infinite-dimensional manifolds are established. These normal form results are new even in finite dimensions. The proo…
Group-valued momentum maps for actions of automorphism groups
Tobias Diez, Tudor S. Ratiu
The space of smooth sections of a symplectic fiber bundle carries a natural symplectic structure. We provide a general framework to determine the momentum map for the action of the…