On the classification of irreducible finite-dimensional representations of $Uq′(so3)$ algebra Available to Purchase

In an earlier work [M. Havlı́ček et al., J. Math. Phys. 40, 2135 (1999)] we defined for any finite dimension five nonequivalent irreducible representations of the nonstandard deformation $Uq′(so3)$ of the Lie algebra $so3$ where q is not a root of unity [for each dimension only one of them (called classical) admits limit $q→1].$ In the first part of this paper we show that any finite-dimensional irreducible representation is equivalent to some of these representations. In the case $qn=1$ we derive new Casimir elements of $Uq′(so3)$ and show that a dimension of any irreducible representation is not higher than n. These elements are Casimir elements of $Uq′(som)$ for all m and even of $Uq′(isom+1)$ due to Inönu–Wigner contraction. According to the spectrum of one of the generators, the representations are found to belong to two main disjoint sets. We give full classification and explicit formulas for all representations from the first set (we call them nonsingular representations). If n is odd, we have full classification also for the remaining singular case with the exception of a finite number of representations.