Ortogonal rotation in theory of finite-dimensional representations of   quantum semisimple algebras. The case of $A_2$ algebra
  The metohod of ortogonal rotations introduced in the previous papers of the author is used for construction of the explicit form the generators of the simple roots for quantum (and ussual) semisimple algebras. All calculations are presented in details for finite-dimensional representation $(p,q)$ of $A^q_2$ algebra. 
A.N.Leznov