Smooth representations of ${GL}_m(D)$. V: Endo-classes
Smooth representations of ${GL}_m(D)$. V: Endo-classes
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${GL}_m(D)$ 的平滑表示。
DOI：
10.4171/dm/360
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发表时间：
2010
影响因子：
0.9
通讯作者：
S. Stevens
中科院分区：
文献类型：
--
作者：
P. Broussous;Vincent S'echerre;S. Stevens
设F是局部紧的非阿基米德局部域。本文将Bushnell和Henniart对GL_n（F）引入的endo-类的概念推广到F上GL_n（n>0）的任何内部形式。我们研究了这些群的简单特征标的交织关系，特别是它们在迁移下的保持性质。这使得我们可以将GL_n（F）的内部形式的任何离散级数表示与F上的endo类联系起来。我们猜想，这endo类是不变的地方Jacquet-Langlands对应。
Let F be a locally compact nonarchimedean local field. In this article, we extend to any inner form of GL_n over F, with n>0, the notion of endo-class introduced by Bushnell and Henniart for GL_n(F). We investigate the intertwining relations of simple characters of these groups, in particular their preservation properties under transfer. This allows us to associate to any discrete series representation of an inner form of GL_n(F) an endo-class over F. We conjecture that this endo-class is invariant under the local Jacquet-Langlands correspondence.