On Gelfand-Zetlin modules over orthogonal Lie algebras

We construct a new family of simple modules over orthogonal complex Lie algebra associated with Gelfand-Zetlin formulae for simple finite dimensional modules and study the corresponding Gelfand-Zetlin subalgebra. 1 Introduction Explicit formulae which effectively define all simple finite dimensional modules over the groups of unimodular and orthogonal matrices were obtained by Gelfand and Zetlin in their famous papers [GZ1, GZ2]. Using these formulae it is possible to define and investigate big families of modules over the corresponding Lie algebras, as was done (for special real forms on the Lie algebras) in [O1, O2]. The analogous formulae are also known for quantum groups (see [J, NT, GK] and references therein). In the same way, using the formulae for the unimodular group, Drozd, Futorny and Ovsienko constructed a large family of simple modules over the reductive Lie algebra G = gl(n; C ) in [DFO1, DFO2]. Roughly speaking this is an n(n + 1)=2-parameter family of simple G-modules ..