Finite dimensional unitary representations of quantum Anti-de Sitter groups at roots of unity
Abstract
We study irreducible unitary \reps of
U
q
(SO(2,1))
and
U
q
(SO(2,3))
for
q
a root of unity, which are finite dimensional. Among others, unitary \reps corresponding to all classical one-particle representations with integral weights are found for
q=
e
iπ/M
, with
M
being large enough. In the "massless" case with spin bigger than or equal to 1 in 4 dimensions, they are unitarizable only after factoring out a subspace of "pure gauges", as classically. A truncated associative tensor product describing unitary many-particle representations is defined for
q=
e
iπ/M
.