Compression of Nakajima monomials in type A and C

Abstract

We describe an explicit crystal morphism between Nakajima monomials and monomials which give a realization of crystal bases for finite dimensional irreducible modules over the quantized enveloping algebra for Lie algebras of type A and C. This morphism provides a connection between arbitrary Nakajima monomials and Kashiwara---Nakashima tableaux. This yields a translation of Nakajima monomials to the Littelmann path model. Furthermore, as an application of our results we define an insertion scheme for Nakajima monomials compatible to the insertion scheme for tableaux.