7 problems

Let $\dot{\mathbb U}$ be the modified form of the level-zero affine quantum group of type $A$, with canonical basis $\dot{\mathbb B}$, and let…

Let $Q$ be a quiver with associated Lie algebra $bmathfrak{g}$, let $Z_W$ be the corresponding Steinberg type variety, and let $b1\mathfrak{g}^{\sigma}$ and $Z_W^{\sigma}$ denote t…

Let $C$ be a symmetrizable generalized Cartan matrix, let $D$ be a symmetrizer of $C$, and let $H=H(C,D,\Omega)$, $\mathcal{M}=\mathcal{M}(H)$, and $\mathfrak{n}=\mathfrak{n}(C)$ b…

Let $C$ be a symmetrizable generalized Cartan matrix, let $D$ be a symmetrizer of $C$, and let $H=H(C,D,\Omega)$ be the associated algebra for an orientation $\Omega$. Let…

Let $\mathrm{\mathbf{econv}}(\mathrm{Gr})_0$ be the subcategory of constructible-function convolutions generated by the relevant Satake-fibre functions, and let…

A locally compact groupoid or quantum groupoid is considered together with convolution products of functions having locally compact support. Conjecture. Similar results to the corr…

Let $\mathcal{S}_{n-k,k}$ be the Slodowy slice, let $Y$ be the corresponding Springer fiber, and let $A$ range over all irreducible components of $Y$. Write…