
Symmetry in Nonlinear Mathematical Physics  2009
Kostyantyn Yusenko (Institute of Mathematics, Kyiv, Ukraine)
Representations of partially ordered sets in Hilbert spaces. Unitarization
Abstract:
Let H be a separable Hilbert space. The system S =(H;H_{1},...,H_{n}) of subspaces
H_{i} of the space H is a representation of some finite
partially ordered set (poset) P in Hilbert space H if
the inclusion between the subspaces corresponds to the partial order
in P and the linear combination of the projections on
corresponding subspaces is equal to scalar operator. The
representation theory of the posets in Hilbert space has deep
interconnections with the representation theory of different object.
For the case when P is primitive and of finite type we investigate
when linear representation can present Hilbert representation.

