Distinguished tame supercuspidal representations and odd orthogonal periods
Distinguished tame supercuspidal representations and odd orthogonal periods
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DOI：
10.1090/s1088-4165-2012-00418-6
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发表时间：
2011-08
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影响因子：
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通讯作者：
J. Hakim;Joshua M. Lansky
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文献类型：
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作者：
J. Hakim;Joshua M. Lansky
我们进一步发展和简化了由Hakim和Murnaghan提出的关于可分辨的归约p-进群超尖角表示的一般理论，以及由Lusztig得到的关于有限约化群的类似理论。我们应用我们的结果研究了$n$奇数域和$F$非阿基米德局部域的表示，它们关于$n$变量的正交群是可区别的。特别地，我们精确地确定关于正交群的超尖球面表示何时是可区别的，如果是这样的话，可区别线性形式的空间有一维。
We further develop and simplify the general theory of distinguished tame supercuspidal representations of reductive $p$-adic groups due to Hakim and Murnaghan, as well as the analogous theory for finite reductive groups due to Lusztig. We apply our results to study the representations of ${\rm GL}_n(F)$, with $n$ odd and $F$ a nonarchimedean local field, that are distinguished with respect to an orthogonal group in $n$ variables. In particular, we determine precisely when a supercuspidal representation is distinguished with respect to an orthogonal group and, if so, that the space of distinguishing linear forms has dimension one.