1 citations · 5 across the 6 of their papers we have counts for
7 papers
On Toric Poisson Structures of Type and their Cohomology
Arlo Caine, Berit Nilsen Givens
We classify real Poisson structures on complex toric manifolds of type and initiate an investigation of their Poisson cohomology. For smooth toric varieties, such structure…
Non-compact groups of inner type and factorization
Arlo Caine, Doug Pickrell
We investigate Birkhoff (or triangular) factorization and (what we propose to call) root subgroup factorization for elements of a noncompact simple Lie group of inner type. F…
Equivalence of Demazure and Bott-Samelson Resolutions via Factorization
Arlo Caine
Let , , and denote a complex semi-simple algebraic group, a Borel subgroup of , and a maximal complex torus in , respectively. Choose a compact real form of …
Loops in noncompact groups and factorization
Arlo Caine, Doug Pickrell
In [11] we showed that a loop in a simply connected compact Lie group has a unique Birkhoff (or triangular) factorization if and only if the loop has a unique root subgro…
Toric Poisson Structures
Arlo Caine
Let X(Σ) be a smooth projective toric variety for a complex torus T_\C. In this paper, a real T_\C-invariant Poisson structure Π_Σis constructed on the complex manifold X(Σ), the s…
Homogeneous Poisson structures on symmetric spaces
Arlo Caine, Doug Pickrell
We calculate, in a relatively explicit way, the Hamiltonian systems which arise from the Evens-Lu construction of homogeneous Poisson structures on both compact and noncompact type…