The Wigner 
-matrix
is the 
unitary matrix
representing an element 
of the special unitary
group 
in its irreducible representation of
dimension 
.
Here, 
for a nonnegative integer 
, and the row and column indices 
and 
range from 
to 
in steps of 1. Its entries are the Wigner
D-functions 
,
commonly parametrized by three Euler angles.
As a group representation, the matrix satisfies
 |
Since it is a unitary matrix,
 |
where the bar denotes the entrywise complex conjugate, 
denotes the transpose,
and 
is the identity matrix. For integer 
, the group
representation also descends to the rotation group 
, the three-dimensional special
orthogonal group.
