Representations of the q-deformed algebra U ′ q (s o 2,2 )
Abstract
The main aim of this paper is to give classes of irreducible infinite dimensional representations and of irreducible
∗
-representations of the q-deformed algebra
U
′
q
(s
o
2,2
)
which is a real form of the non-standard deformation
U
′
q
(s
o
4
)
of the universal enveloping algebra
U(so(4,C))
. These representations are described by two complex parameters and are obtained by "analytical continuation" of the irreducible finite dimensional representations of the algebra
U
′
q
(s
o
4
)
in the basis corresponding to the reduction from
U
′
q
(s
o
4
)
to
U(s
o
2
⊕s
o
2
)
.