Schensted-Type Correspondence, Plactic Monoid, and Jeu de Taquin for Type Cn

We use Kashiwaraʹs theory of crystal bases to study the plactic monoid for Uq(sp2n). Then we describe the corresponding insertion and sliding algorithms. The sliding algorithm is essentially the symplectic Jeu de Taquin defined by Sheats and our construction gives the proof of its compatibility with plactic relations.