The RTT realization for the deformed gl(2|2) Yangian

Abstract

In this paper we work out the RTT realization for the Yangian algebra of the Hubbard model and anti-de Sitter/conformal field theory correspondence. We find that this Yangian algebra is of a non-standard type in which the levels of the Yangian mix. The crucial feature that allows this is a braiding factor that deforms the coproduct and generates the central extensions of the underlying gl(2|2) Lie algebra. In our RTT realization we have also been able to incorporate the so-called secret symmetry and we were able to extend it to higher Yangian levels. Finally, we discuss the center of the Yangian and the automorphisms related to crossing symmetry.