关于Alvis-Curtis对偶的Okuyama定理

Alvis-Curtis Duality for Representations of Reductive Groups with Frobenius Maps

We generalize the Alvis-Curtis duality to the abstract representations of reductive groups with Frobenius maps. Similar to the case of representations of finite reductive groups, we show that the Alvis-Curtis duality of infinite type which we define in this paper also interchanges the irreducible representations in the principal representation category.

关于分解数与Alvis-Curtis对偶

On decomposition numbers and Alvis-Curtis duality

我们证明了对于一般线性群${\rm GL}_n(q)$以及$q$ -Schur代数，特征$\ell$，$\ell \nmid q$的域上的模Alvis-Curtis对偶的知识等价于分解数的知识.

Alvis-Curtis Duality for Finite General Linear Groups and a Generalized Mullineux Involution

We study the effect of Alvis-Curtis duality on the unipotent representations of $\mathrm{GL}_n(q)$ in non-defining characteristic $\ell$. We show that the permutation induced on the simple modules can be expressed in terms of a generalization of the Mullineux involution on the set of all partitions, which involves both $\ell$ and the order of $q$ modulo $\ell$.

Alvis-Curtis对偶、中心特征标和实值特征标

Alvis-Curtis duality, central characters, and real-valued characters

我们证明了Alvis-Curtis对偶保持了具有连通中心的李型连通约化群特征标的Frobenius-Schur指标。这使得我们可以推广D. Prasad，它将正则实值特征的Frobenius-Schur指标与其中心特征联系起来。我们应用这些结果来计算某些实值，不可约，Frobenius不变Deligne-Lusztig字符的Frobenius-Schur指标，和有限酉群的实值正则和半单字符的Frobenius-Schur指标。

一般线性群的权2块与模Alvis-Curtis对偶

Weight 2 blocks of general linear groups and modular Alvis-Curtis duality

给出了q-Schur代数的权2块和[2：1]-对的结构，并明确计算了有限一般线性群的权2块在非定义特征下的模Alvis-Curtis对偶.

Deligne-Lusztig簇的交上同调的Alvis-Curtis对偶的正性猜想

A positivity conjecture for the Alvis-Curtis dual of the intersection cohomology of a Deligne-Lusztig variety

我们制定了一个强的正猜想所提供的Alvis-Curtis对偶的Deligne-Lusztig品种的交叉上同调的字符。这个猜想为确定有限约化群的幂幺$\ell$ -块的分解数提供了一个有力的工具。