Decomposition Theorem for Product of Fundamental Crystals in Monomial Realization of type $C_n$

Abstract

We consider a product of fundamental crystals of type $C_n$ in monomial realization, where the product means a natural product of Laurent monomials, not a tensor product. Then we shall show that the product still holds a crystal structure and describe how it is decomposed into irreducible crystals, which is, in general, different from the decomposition rule for the tensor product of the fundamental crystals.

35 pages