Extended Nakajima monomials and crystal for finite simple Lie algebras

Nakajima introduced a certain set of monomials realizing the irreducible highest weight crystals . The monomial set can be extended so that it contains the crystal in addition to . We study the crystal base of the negative part of a quantum group. For finite types Bn, Cn, Dn, and G2, we present new descriptions of the crystal in the language of extended Nakajima monomials. There is a natural correspondence between the monomial description and Young tableau description, which is another description of .