We consider a product of fundamental crystals of type A in monomial realization. Then we shall show that the product holds crystal structure and describe how it is decomposed into irreducible crystals, which is, in general, different from the decomposition for tensor product of the fundamental crystals.
"Decomposition Theorem for Product of Fundamental Crystals in Monomial Realization." Tokyo J. Math. 43 (1) 239 - 258, June 2020. https://doi.org/10.3836/tjm/1502179324