6 problems

Standard Q-Koszul conjecture. The algebra $\widetilde{\operatorname{gr}} A$ is standard Q-Koszul.

Standard Q-Koszul conjecture. The algebra $\widetilde{\operatorname{gr}} A$ is standard Q-Koszul.

Retain the hypotheses and notation of Conjecture II. Let $A'$ be the quasi-hereditary quantum quotient algebra and let $\operatorname{gr} A'$ be its associated graded algebra. Conj…

Conjecture IIa. These three equalities hold. In part (2), $\widetilde{\operatorname{gr}}^\diamond\nabla(\lambda)$ is the costandard module for $\lambda$ in the highest-weight categ…

Conjecture II. These identities hold. The Ext groups may equivalently be computed over the corresponding enveloping algebra $U_\zeta$ or algebraic group $G$. Several cases are know…

Let $G$ be a semisimple, simply connected algebraic group, defined and split over ${\mathbb F}_p$, where $p$ is a prime that is KL-good for the root system $R$ of $G$. Let $\Gamma$…