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Semisimple characters for inner forms II: Quaternionic forms of 𝑝-adic classical groups (𝑝 odd)
Representation Theory ( IF 0.6 ) Pub Date : 2020-07-29 , DOI: 10.1090/ert/544 Daniel Skodlerack
Representation Theory ( IF 0.6 ) Pub Date : 2020-07-29 , DOI: 10.1090/ert/544 Daniel Skodlerack
Abstract:In this article we consider the set 
of rational points of a quaternionic form of a symplectic or an orthogonal group defined over a non-
Archimedean local field of odd residue characteristic. We construct all full self-dual semisimple characters for
and we classify their intertwining classes using endo-parameters. We compute the set of intertwiners between self-dual semisimple characters, and prove an intertwining and conjugacy theorem. Finally we count all 
-intertwining classes of full self-dual semisimple characters which lift to the same 
-intertwining class of a full semisimple character for the ambient general linear group 
for 
.
中文翻译：
内部形式的半简单字符II：𝑝-adic古典群的四元离子形式（𝑝奇数）
摘要：在本文中，我们考虑在奇数残基特征的非
阿基米德局部场上定义的辛或正交基团的四元数形式的有理点集。我们为构建所有完全对偶半简单字符，并使用内参数对它们交织的类进行分类。我们计算了自对偶半简单字符之间的交织集，并证明了交织和共轭定理。最后，我们计算所有的全自偶半单字符，提升到同-intertwining类-intertwining类环境一般线性群全半单字符的。
更新日期：2020-08-25
of rational points of a quaternionic form of a symplectic or an orthogonal group defined over a non-Archimedean local field of odd residue characteristic. We construct all full self-dual semisimple characters for
and we classify their intertwining classes using endo-parameters. We compute the set of intertwiners between self-dual semisimple characters, and prove an intertwining and conjugacy theorem. Finally we count all -intertwining classes of full self-dual semisimple characters which lift to the same -intertwining class of a full semisimple character for the ambient general linear group for . 中文翻译：
内部形式的半简单字符II：𝑝-adic古典群的四元离子形式（𝑝奇数）
摘要：在本文中，我们考虑在奇数残基特征
的非阿基米德局部场上定义的辛或正交基团的四元数形式的有理点集。我们为构建所有完全对偶半简单字符，
并使用内参数对它们交织的类进行分类。我们计算了自对偶半简单字符之间的交织集，并证明了交织和共轭定理。最后，我们计算所有的全自偶半单字符，提升到同-intertwining类-intertwining类环境一般线性群全半单字符的。 
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