  In the context of a canonical quantization of general relativity, one can
deform the loop gravity phase space on a graph by replacing the T*SU(2) phase
space attached to each edge by SL(2,C) seen as a phase space. This deformation
is supposed to encode the presence of a non-zero cosmological constant. Here we
show how to parametrize this phase space in terms of spinor variables, thus
obtaining deformed spinor networks for loop gravity, with a deformed action of
the gauge group SU(2) at the vertices. These are to be formally interpreted as
the generalization of loop gravity twisted geometries to a hyperbolic
curvature.
