4 problems

Let $\mathfrak{g}$ be a complex semisimple Lie algebra, let $M(\lambda)$ and $M(\mu)$ be Verma modules, and let $M(\mu)\hookrightarrow M(\lambda)$ be an embedding. Let $\rho$ denot…

Let $X=X({\mathcal O},{\mathcal L})$ be a standard module with Jantzen filtration … Let $P_{({\mathcal O},{\mathcal L}),({\mathcal O}',{\mathcal L}')}(q)$ be the Kazhdan–Lusztig po…

Let $M_\kappa(\lambda)$ be the module associated with a weight $\lambda$, equipped with its Jantzen filtration and radical filtration. Jantzen–radical filtration conjecture. For an…

Let $W$ be a Weyl group with associated affine Weyl group $W_p$, and let $n_{\lambda\mu}$ be the parabolic Kazhdan–Lusztig polynomial associated to $W\subset W_p$. In the Hecke alg…