This freedom means that projective representations of quantum states are important in quantum theory.

The projective representations of alternating and symmetric groups are the subject of the book .

In particular, the space of spinors is a projective representation of the orthogonal group.

In other words, a projective representation is a representation modulo the center.

The interest for algebra is in the process in the other direction: given a projective representation, try to 'lift' it to a conventional linear representation.

Mathematically speaking, these matrices furnish a unitary projective representation of the rotation group SO(3).

The projective representation of the restricted symplectic group can be constructed directly on coherent states as in the finite-dimensional case.

It will turn out to be a projective representation.

It can be checked that the mapping is a projective unitary representation.

(More generally, it may be a projective representation, which amounts to a representation of the double cover of the group.)