q-deformed algebras U q (s o n ) and their representations
Abstract
For the nonstandard
q
-deformed algebras
U
q
(s
o
n
)
, defined recently in terms of trilinear relations for generating elements, most general finite dimensional irreducible representations directly corresponding to those of nondeformed algebras
so(n)
(i.e., characterized by the same sets of only integers or only half-integers as in highest weights of the latter) are given explicitly in a
q
-analogue of Gel'fand-Tsetlin basis. Detailed proof, for
q
not equal to a root of unity, that representation operators indeed satisfy relevant (trilinear) relations and define finite dimensional irreducible representations is presented. The results show perfect suitability of the Gel'fand-Tsetlin formalism concerning (nonstandard)
q
-deformation of
so(n)
.