6 problems

Let $D^b_{\operatorname{GL}_n}(\operatorname{GL}_n)$ be the bounded equivariant derived category of the algebraic group $\operatorname{GL}_n$, equipped with its canonical braided m…

The character-sheaf duality and perversity conjecture. For every minimal idempotent $e$, there exists $n_e\in\\{0,1,\dotsc,\dim G\\}$ such that

Let $\mathfrak g_{\operatorname{aff},\varsigma}$ be the affine Lie algebra associated with $\mathfrak g',\sigma$, and $\zeta$, and let…

Let $k$ be an algebraically closed field, let $X$ be a projective variety with an action of a linear algebraic group $G$, and suppose that $X$ has finitely many $G$-orbits. Let…

Let $X$ be a smooth variety over an algebraically closed field of characteristic zero, and let a finite group $G$ act effectively on $X$. For $\lambda\in G/{\sim}$, let $X_\lambda$…

Conjecture A. There exists a semiorthogonal decomposition of $D^b_G(X)$ whose pieces ${\cal C}_{[g]}$ are indexed by the conjugacy classes $[g]$ in $G$ and satisfy