2 problems

Cosmall-root characterization conjecture. Assume that $R$ is simply laced and let $\alpha\in R^+\setminus R^{+}_P$. Then $\alpha$ is $P$-cosmall if and only if

Let $M=G/P_M$ be any flag variety. For $u\bin W$, $w\bin W^{\mathrm{comin}}$, with $I(w)\cap\Delta=\{\beta\}$, let $\beta$ be the cominuscule simple root and set … Here…