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We consider the quantum Gelfand invariants which first appeared in a landmark paper by Reshetikhin et al. [Algebra Anal. 1(1), 178–206 (1989)]. We calculate the eigenvalues of the invariants acting in irreducible highest weight representations of the quantized enveloping algebra for g l n . The calculation is based on Liouville-type formulas relating two families of central elements in the quantum affine algebras of type A. [ABSTRACT FROM AUTHOR]

An explicit isomorphism between the R-matrix and Drinfeld presentations of the quantum affine algebra in type A was given by Ding and Frenkel [Commun. Math. Phys. 156, 277–300 (1993)]. We show that this result can be extended to types B, C, and D and give a detailed construction for type C in this paper. In all classical types, the Gauss decomposition of the generator matrix in the R-matrix presentation yields the Drinfeld generators. To prove that the resulting map is an isomorphism, we follow the work of Frenkel and Mukhin [Sel. Math. 8, 537–635 (2002)] in type A and employ the universal R-matrix to construct the inverse map. A key role in our construction is played by a homomorphism theorem, which relates the quantum affine algebra of rank n − 1 in the R-matrix presentation with a subalgebra of the corresponding algebra of rank n of the same type. [ABSTRACT FROM AUTHOR]

We prove that the action of the Yangian algebra Y(slN) is better described by the principal generators on the tensor product of the fundamental representation and its dual. The generalized Bell states or maximally entangled states are permuted by the principal generators in a dramatically simple manner on the tensor product. Under the Yangian symmetry the new quantum number J2 is also explicitly computed, which gives an explanation for these maximally entangled states. [ABSTRACT FROM AUTHOR]

We prove that the action of the Yangian algebra Y(slN) is better described by the principal generators on the tensor product of the fundamental representation and its dual. The generalized Bell states or maximally entangled states are permuted by the principal generators in a dramatically simple manner on the tensor product. Under the Yangian symmetry the new quantum number J2 is also explicitly computed, which gives an explanation for these maximally entangled states. [ABSTRACT FROM AUTHOR]