Monomial Realization of the Tensor Product of Crystals for Quantum Finite Algebras

In this paper, we give a combinatorial description of the crystal bases of the tensor products of the irreducible highest weight modules over quantum finite algebras in terms of Nakajima monomials. Also, we explain how to decompose the tensor product of irreducible highest weight crystals into irreducibles by giving a bijection defined by multiplication of monomials.