Abstract
We construct generic Gelfand-Tsetlin representations of the [Formula: see text]quantum groups [Formula: see text] and [Formula: see text]. These representations are infinite-dimensional analogs to the finite-dimensional irreducible representations provided by Gavrilik and Klimyk in [[Formula: see text]-deformed orthogonal and pseudo-orthogonal algebras and their representations, Lett. Math. Phys. 21 (1991) 215–220]. They are quantum analogs of generic Gelfand-Tsetlin representations constructed by Mazorchuk in [On Gelfand-Zetlin modules over orthogonal Lie algebras, Algebra Colloq. 8 (2001) 345–360]. We give sufficient conditions for irreducibility and provide an upper bound for the length with the help of Casimir elements found by Molev, Ragoucy and Sorba.
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call