A representation of the central extension of the unitary Lie algebra coordinated with a skew Laurent polynomial ring is constructed using vertex operators over an integral Z_2-lattice. The irreducible decomposition of the representation is explicitly
computed and described. As a by-product, some fundamental representations of affine Kac-Moody Lie algebra of type $A_n^{(2)}$ are recovered by the new method.
Motivated to simplify the structure of tensor representations we give a new set of generators for the Yangian $Y(sl(n))$ using the principal realization in simple Lie algebras. The isomorphism between our new basis and the standard Cartan-Weyl basis
is also given. We show by example that the principal basis simplifies the Yangian action significantly in the tensor product of the fundamental representation and its dual.
We propose a quantum analogue of a Tits-Kantor-Koecher algebra with a Jordan torus as an coordinated algebra by looking at the vertex operator construction over a Fock space.
