Decomposition Theorem for Product of Fundamental Crystals in Monomial Realization

TL;DR

This paper proves a decomposition theorem for the product of fundamental crystals in monomial realization of type A, showing how it breaks into irreducible crystals, differing from tensor product decompositions.

Contribution

It introduces a new decomposition theorem for fundamental crystals in monomial realization, distinct from tensor product decompositions.

Findings

Product of fundamental crystals forms a crystal structure.

Decomposition into irreducible crystals is explicitly described.

Decomposition differs from tensor product decompositions.

Abstract

We consider a product of fundamental crystals in monomial realization of type A. 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.