Standard λ-lattices from quantum groups

Abstract.

A large family of standard λ-lattices in the sense of Sorin Popa is obtained from the representations of quantum groups. When the deformation parameter q of the quantum group is a positive real number, the standard λ-lattice so obtained is of infinite depth. When q is a certain root of unity and quantum group is of type A, B, C or D, our approach is different from that of H. Wenzl and should agree with his results. We also obtain finite depth standard λ-lattices from quantum groups of type G ₂, E ₆, E ₇ and all the spinor representations of type B and D simple Lie algebras.