# Relationship between crystal root operators and usual $e_i, f_i$?

Suppose I am working in a symmetrizable Kac–Moody Lie algebra $$\mathfrak{g}$$. Let $$e_1,\dotsc,e_n,f_1,\dotsc,f_n$$ denote the usual Chevalley generators of $$\mathfrak{g}$$. Let $$V$$ be a highest weight irreducible representation with a crystal basis $$B$$. On $$B$$ I have the crystal operators $$\tilde e_1, \dotsc, \tilde e_n, \tilde f_1, \dotsc, \tilde f_n$$. I know that the crystal root operators have the same grades as their corresponding Chevalley generators. i.e, $$e_i,\tilde e_i:(V_\mu) \to V_{\mu+\alpha_i}$$, and $$f_i,\tilde f_i:(V_\mu) \to V_{\mu-\alpha_i}$$ for $$i=1,2,\dotsc,n$$.

But beyond this, what relation do the crystal operators have with the corresponding Chevalley generator?

In particular, I am interested to know: if a relation of the form $$\textbf{word in crystal operators}\cdot v= 0$$ holds in $$B$$, where $$v$$ denotes the highest weight vector, then what does it say at the level of representations and the corresponding word in the Chevalley generators?