论文标题
诱发表示形式的拉福格品种和不可还原性
The Lafforgue variety and irreducibility of induced representations
论文作者
论文摘要
我们构建了Lafforgue Variety，这是一种配备了开放密集的亚cheme的仿射方案，即在任何字段$ k $上的非交换Unital Algebra $ r $的简单模块，前提是中心$ z（r）$有限地生成，并且$ r $是$ z（r）$ - 模块的，$ r $是有限生成的。我们的主要技术工具是对非共同代数的希尔伯特计划的概括，这可能具有独立的利益。 在Bernstein组件的Hecke代数的情况下，应用我们的构建，我们在伯恩斯坦品种上的普遍歧视因素消失方面得出了诱发表示不可约性的特征。在一个分裂还原$ p $ adic group的iWahori-hecke代数的情况下，我们明确计算了判别物。
We construct the Lafforgue variety, an affine scheme equipped with an open dense subscheme parametrizing the simple modules of a non-commutative unital algebra $R$ over any field $k$, provided that the center $Z(R)$ is finitely generated and $R$ is finitely generated as a $Z(R)$-module. Our main technical tool is a generalization of the Hilbert scheme for non-commutative algebras, which may be of independent interest. Applying our construction in the case of Hecke algebras of Bernstein components, we derive a characterization for the irreducibility of induced representations in terms of the vanishing of a generalized discriminant on the Bernstein variety. We explicitly compute the discriminant in the case of an Iwahori-Hecke algebra of a split reductive $p$-adic group.
