Statement of the Alexandru Conjecture

Introduction to the Alexandru Conjecture

Is a Verma module transformed into another Verma module by a selfequivalence? The answer is affirmative and the proof suggests a notion of standard object in the category of Harish-Chandra modules that coincides often, but not always, with the usual one.

A Generalization of the Auslander-Reiten Conjecture for the Bounded Derived Category

We study the bounded derived category $\D^b(\Rmod)$ of a left Noetherian ring $R$. We give a version of the Generalized Auslander-Reiten Conjecture for $\D^b(\Rmod)$ that is equivalent to the classical statement for the module category and is preserved under derived equivalence.

Hikita conjecture for the minimal nilpotent orbit

We check that the statement of Hikita conjecture holds for the case of the minimal nilpotent orbit of a simple Lie algebra $\mathfrak{g}$ of type ADE and $\mathbb{C} ^2 / Γ$.

Donovan's conjecture and blocks with abelian defect groups

We give a reduction of Donovan's conjecture for abelian groups to a similar statement for quasisimple groups. Consequently we show that Donovan's conjecture holds for abelian $2$-groups.

阿尔佩林重量猜想与盖拉布曼对应关系 via 特征标三元组

The Alperin Weight Conjecture and the Glauberman correspondence via character triples

本文通过特征标三元组验证了纳瓦罗猜想，并将其简化为单列群问题，证明了若干类群和块的结论。