3 problems

Multiplicative compatibility conjecture. The isomorphism $\operatorname{End}_{\mathfrak{g}}(P)\cong H^*(\psi(P))$ is a ring homomorphism, and the isomorphism

Let $X=T^*(G/B)$ be the Springer resolution of the nilpotent cone $Y={\mathcal N}\subset{\mathfrak g}^*$ in the coadjoint representation of a semisimple algebraic group $G$, let…

Lehrer–Shoji's conjecture. Suppose that $e$ is a regular nilpotent in a Levi subalgebra. Then, for every $i=0,1,\ldots,\ell$,