4 citations · 7 across the 8 of their papers we have counts for
8 papers
The de Rham cohomology of a Lie group modulo a dense subgroup
Brant Clark, Francois Ziegler
Let be a dense subgroup of a Lie group with Lie algebra . We show that the (diffeological) de Rham cohomology of equals the Lie algebra cohomology of $\m…
Remarks on Diffeological Frobenius Reciprocity
Gabriele Barbieri, Jordan Watts, Francois Ziegler
A recent paper [R22] established "Frobenius reciprocity" as a bijection between certain symplectically reduced spaces (which need not be manifolds), and conjectured: 1°) is…
Relativity without light: A new proof of Ignatowski's theorem
Jean-Philippe Anker, Francois Ziegler
V. Ignatowski (1910) showed that assumptions about light are not necessary to obtain Lorentzian kinematics as one of only few possibilities. We give a much simplified proof of his…
Symplectic Induction, Prequantum Induction, and Prequantum Multiplicities
Tudor S. Ratiu, Francois Ziegler
Frobenius reciprocity asserts that induction from a subgroup and restriction to it are adjoint functors in categories of unitary G-modules. In the 1980s, Guillemin and Sternberg es…
Explicit Pseudo-Kähler Metrics on Flag Manifolds
Thomas Mason, Francois Ziegler
The coadjoint orbits of compact Lie groups each carry a canonical (positive definite) Kähler structure, famously used to realize the group's irreducible representations in holomorp…
Symplectic Mackey Theory
Francois Ziegler
Many years ago Kazhdan, Kostant and Sternberg defined the notion of inducing a hamiltonian action from a Lie subgroup. In this paper, we develop the attendant imprimitivity theorem…
Localized Quantum States
Francois Ziegler
Let X be a symplectic manifold and Aut(L) the automorphism group of a Kostant-Souriau line bundle on X. *Quantum states for X*, as defined by J.-M. Souriau in the 1990s, are certai…
Primary Spaces, Mackey's Obstruction, and the Generalized Barycentric Decomposition
Patrick Iglesias-Zemmour, Francois Ziegler
We call a hamiltonian N-space \emph{primary} if its moment map is onto a single coadjoint orbit. The question has long been open whether such spaces always split as (homogeneous) x…