  We develop an Hamiltonian representation of the sl(2,C) algebra on a phase
space consisting of N copies of twistors, or bi-spinors. We identify a complete
set of global invariants, and show that they generate a closed algebra
including gl(N,C) as a subalgebra. Then, we define the linear and quadratic
simplicity constraints which reduce the spinor variables to (framed) 3d
spacelike polyhedra embedded in Minkowski spacetime. Finally, we introduce a
new version of the simplicity constraints which (i) are holomorphic and (ii)
Poisson-commute with each other, and show their equivalence to the linear and
quadratic constraints.
