11 problems

Transitivity conjecture. The group spanned by mutations of exceptional bases and the isometries of $K_0(\mathbb{P}_n)$ acts transitively on the set of exceptional bases of…

Let $e$ be a distinguished nilpotent element, so that $A_e=Q_e$, and let $c$ be the corresponding two-sided cell. Let $J_c$ be identified with…

Let $\mathcal{A}$ be the algebra generated by the elements $R_{\mathbf d}$ over $\mathbb{Z}[q_1^{\pm1},q_2^{\pm1}]$, and specialize its parameters by … Let…

Symmetric-power criterion conjecture. If the canonical morphism above is an isomorphism, then $\pi$ is an isomorphism.

Let $cmathfrak{M}$ be the set of multisegments, let $cLambda(cmathfrak{m})$ be the RSK-standard representation attached to $cmathfrak{m}cincmathfrak{M}$, and let $cmathcal{R}'$ be…

Let $K^n(\operatorname{\mathcal{U}})$ be the free abelian group generated by isomorphism classes of direct summands of $H^*V_n$, where $V_n=(\operatorname{\mathbb{F}}_p)^n$, and le…

Let $A$ be an abelian variety of dimension $g$, let $K=K_0(A)\otimes\mathbf Q$, and let $\operatorname{Fil}^r_\Gamma$ be the gamma filtration associated with the composed lambda-ri…

Let $A$ be an abelian variety of dimension $g$ over an algebraically closed field of characteristic zero, and let $K_0(A)\otimes\mathbf Q$ carry its usual gamma filtration…

Let $\bD$ be the divided power algebra over $\bk$, let $R$ be the relevant grading ring, and let $\cC_n$ be the category of finitely generated $\bk$-modules supported on…

Distinct-extension conjecture. Any such extension decategorifies an extension of the ground field as above, and if $\mathcal{A}$ and $\mathcal{A}'$ are distinct sub-Hopf algebras,…

Let $\mathfrak{g}=\mathfrak{spo}(2n|2m+1)$, and let $\mathfrak{p}$ be the maximal parabolic subalgebra obtained by removing the simple root $\epsilon_m$, with Levi subalgebra…