Looking at a few of Littelmann's papers, he seems to only apply root operators $f_\alpha$ for $\alpha$ a simple root. However, the definition seems to make perfect sense for $\alpha$ any positive root. (Indeed one can change the hyperplane that divides positive and negative roots and get a new set of simple roots corresponding to that choice.)

My question is: how much have the $e_\alpha$ and $f_\alpha$ been studied or used for nonsimple $\alpha$?
(This question also applies to other path models, like LS paths.)