Theorem 1.2 is now proved, but we have further important remarks to make, which will occupy the last three chapters. These chapters may be read independently of each other.
In this chapter, we will translate Statements A and B from Chapter 6 into Statements A′ and B′ in the language of crystal bases, and explain in this language how Statement B′ implies Statement A′.
We slightly generalize the definition (2.14) by considering more general reduced words Ω and defining
This definition is provisional since it assumes that we can give an appropriate definition of boxing and circling for Ω. We will only ...