6 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…

Let $G$ be a reductive algebraic group over $\C$, let $u$ be a unipotent element of $G$, and let $\cb_u$ be its Springer fibre, the variety of Borel subgroups containing $u$. Sprin…

Let $G$ be the reductive group, $\mathcal{B}$ its flag variety, and $G_{\ge0}$ its totally nonnegative part. For $g\in G_{\ge0}$, let $\mathcal{B}_{g,\ge0}$ be the totally nonnegat…

The W-algebra realization conjecture. There exists an isomorphism of vector spaces

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