On the unicity of types for tame toral supercuspidal representations
On the unicity of types for tame toral supercuspidal representations
复制标题
论驯服的口腔上尖端表征类型的单一性
DOI：
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
M. Nevins
中科院分区：
文献类型：
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作者：
P. Latham;M. Nevins
对于驯服的任意长度的toral，也称为正正则，超尖点表示的单连通和半单p-adic群G，根据Adler-Yu构造，我们确定哪些组件的限制到一个极大的紧子群的类型。我们给出了存在唯一这样的分量的条件，然后给出了一类不存在的例子，反驳了极大紧开子群类型唯一性猜想的强版本。我们重申了唯一性猜想，并证明了它持有的集团和表示下考虑的一个温和的条件下的深度。
For tame arbitrary-length toral, also called positive regular, supercuspidal representations of a simply connected and semisimple p-adic group G, constructed as per Adler-Yu, we determine which components of their restriction to a maximal compact subgroup are types. We give conditions under which there is a unique such component, and then present a class of examples for which there is not, disproving the strong version of the conjecture of unicity of types on maximal compact open subgroups. We restate the unicity conjecture, and prove it holds for the groups and representations under consideration under a mild condition on depth.