An insertion scheme for C n crystals

Introduction The concept of the crystal basis [8] of a representation of quantum (affine) Lie algebras has proved very useful in examining the structure of such representations[6]. The crystal bases for the finite-dimensional irreducible representations of the quantum group U q (g) where g is one of the classical Lie algebras A n , B n , C n or D n , were explicitly described by Kashiwara and Nakashima [9] in terms of tableaux. The tensor product rule for crystals allows the decomposition of tensor products of crystals in terms of irreducible crystals to be described in a combinatorial fashion [19]. The action of the Kashiwara operators ~ e i , ~ f i on the tensor product of two crystals is given by [7] ~ f i (b 1\Omega