23 citations · 149 across the 33 of their papers we have counts for
6 papers · 1 filter
The Toric Geometry of Triangulated Polygons in Euclidean Space
Benjamin Howard, Christopher Manon, John Millson
Speyer and Sturmfels [SpSt] associated Gröbner toric degenerations $\mathrm{Gr}_2(\C^n)^{\tree}$ of $\mathrm{Gr}_2(\C^n)$ to each trivalent tree $\tree$ with leaves. These dege…
The Chevalley Involution and a Duality of Weight Varieties
Benjamin J. Howard, John J. Millson
We study the action of the Chevalley involution of a simple complex Lie group G on the set of its weight varieties (i.e. torus quotients of its flag manifolds). We find for torus q…
The generalized triangle inequalities for rank 3 symmetric spaces of noncompact type
Shrawan Kumar, Bernhard Leeb, John J. Millson
We compute the generalized triangle inequalities explicitly for all rank 3 symmetric spaces. We find that for Sp(6) the corresponding polyhedral cone has 102 facets and 51 edges.
Bending flows for sums of rank one matrices
Hermann Flaschka, John Millson
We study certain symplectic quotients of n-fold products of complex projective m-space by the unitary group acting diagonally. After studying nonemptiness and smoothness these quot…
Quantization of bending deformations of polygons in Euclidean space, hypergeometric integrals and the Gassner representation
Michael Kapovich, John J. Millson
We quantize the bending deformations of n-gon linkages by linearizing the bending fields at a degenerate n-gon to get a representation of the Malcev Lie algebra of the pure braid g…
The symplectic geometry of polygons in hyperbolic 3-space
Michael Kapovich, John J. Millson, Thomas Treloar
We study the symplectic geometry of the moduli space of closed n-gons with fixed side-lengths in hyperbolic 3-space. We prove that these moduli spaces have a symplectic structure c…