## conditions under which a $(L-S)$ path is undefined.

Let $\pi$ be a Lakshmibai seshadri $(L-S)$ path of weight $\lambda$ .Let $B_{\pi}$ be the set of paths obtained from $\pi$ by applying the root operatos.It is known that the formal character of $B_{\pi}$ is equal to the character of simple module of highest weight $\lambda$ of a symmetrizable kac moody algebra $L$. $B_{\pi}$ is equal to the set of paths obtained from $\lambda$ by applying lowering operators corresponding to different simple roots of $L$. let $f^a_{\alpha_1}.f^b_{\alpha_2}...f^t_{\alpha_n}.\pi$ be a path in $B_{\pi}$.under what conditions on $a$,$b$,... $t$ the path $f^a_{\alpha_1}.f^b_{\alpha_2}...f^t_{\alpha_n}.\pi$ is undefined where $a$,$b$,$c$... $t$ are non negative integers?Is it possible to find such conditions at least for rank 2 case?

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