3 problems

Let $G=Sp(2n,\mathbb{R})$ or $SO^*(2n)$, let $\pi_u=X(r,s;\epsilon,\eta)$ be a non-trivial special unipotent representation associated with the partition $[2^{2k}1^{2n-2k}]$, and l…

Huang's conjecture. For any irreducible $(\mathfrak{g},K)$-module $X$, there should be no cancellation between $H_D^+(X)$ and $H_D^-(X)$.

Translation principle conjecture. Assume that the $W_{\frak{g}}$-representation $\sigma_K$ generated by the Weyl dimension formula for $\frak{k}$ corresponds to a nilpotent…