Explicit asymptotic expansions for tame supercuspidal characters
Explicit asymptotic expansions for tame supercuspidal characters
复制标题
驯服超尖角特征的显式渐近展开
DOI：
10.1112/s0010437x18007364
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发表时间：
2017
影响因子：
1.8
通讯作者：
Loren Spice
中科院分区：
文献类型：
--
作者：
Loren Spice
我们结合联合收割机的想法Harish-Chandra-Howe当地的字符扩展，它可以集中在一个任意的半单元素，和一个Kim-Murnaghan渐近展开，到目前为止，已被认为只有周围的身份。我们发现，对于大多数光滑，不可约的表示（那些包含一个良好的，最小的K型），金-Murnaghan型渐近展开是有效的明确定义的邻域几乎任意的半单元素。然后，我们给出了一个明确的，归纳配方计算系数的渐近展开的驯服超尖点表示。在归纳步骤中唯一需要的额外信息是单位的第四根，我们希望这在证明稳定性和内观转移恒等式中是有用的。
We combine the ideas of a Harish-Chandra–Howe local character expansion, which can be centred at an arbitrary semisimple element, and a Kim–Murnaghan asymptotic expansion, which so far has been considered only around the identity. We show that, for most smooth, irreducible representations (those containing a good, minimal K-type), Kim–Murnaghan-type asymptotic expansions are valid on explicitly defined neighbourhoods of nearly arbitrary semisimple elements. We then give an explicit, inductive recipe for computing the coefficients in an asymptotic expansion for a tame supercuspidal representation. The only additional information needed in the inductive step is a fourth root of unity, which we expect to be useful in proving stability and endoscopic-transfer identities.