6 problems

Let $G\,|\,V$ be a polar representation, let $f:V\to Q$ be its quotient map, and write $V^\circ=f^{-1}(Q^{reg})$. Let $V^s$ denote the stable vectors and $V^{rs}$ the regularly sem…

Nonexistence conjecture. A $V$-regular point cannot fail to be regular; equivalently, the rank-zero case for $(K,S)$ cannot occur.

Let $(G,V)$ be a visible stable polar representation for a connected reductive group $G$. Let $\pi\colon V\to V/\!/G$ be the quotient map, let $P$ be its nearby cycles sheaf, let…

Let $G \mathbin{|} V$ be a polar representation of a connected reductive algebraic group over $\mathbb{C}$, let $C$ be a Cartan subspace, and let $W=N_G(C)/Z_G(C)$ be its Weyl grou…

Let $(G,V)$ be a polar representation of a reductive algebraic group, with Cartan subspace ${\mathfrak c}$ and Weyl group $W$. The natural morphism … where…

Cartan-subspace quotient conjecture. The map $\pi$ sets up a one-to-one correspondence between the $G_{\mathbf R}$-conjugacy classes of Cartan subspaces of $V_{\mathbf R}$ and the…