For a tame supercuspidal representation π \pi of a connected reductive p p -adic group G G , we establish two distinct and complementary sufficient conditions, formulated in terms of the geometry of the Bruhat–Tits building of G G , for the irreducible components of its restriction to a maximal compact subgroup to occur in a representation of G G which is not inertially equivalent to π \pi . The consequence is a set of broadly applicable tools for addressing the branching rules of π \pi and the unicity of [ G , π ] G [G,\pi ]_G -types.

中文翻译：

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Bruhat-Tits 建筑物中通过不动点集的典型表示

对于连接的还原 pp -adic 群 GG 的驯服的超尖表示 π \pi，我们建立了两个不同且互补的充分条件，根据 GG 的 Bruhat-Tits 构建的几何形状来表述，用于其限制的不可约成分出现在 GG 的表示中的最大紧子群，它在惯性上不等价于 π \pi 。结果是一组广泛适用的工具，用于解决 π \pi 的分支规则和 [ G , π ] G [G,\pi ]_G 类型的唯一性。