On the correspondence of representations between $GL(n)$ and division algebras
On the correspondence of representations between $GL(n)$ and division algebras
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关于$GL(n)$与除法代数表示的对应关系
DOI：
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
A. Raghuram
中科院分区：
文献类型：
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作者：
Joshua M. Lansky;A. Raghuram
对于p-adic域F上的除代数D，我们证明了在GL n（F）的离散级数表示和D* 的不可约表示的对应下，深度是保持不变的.我们还证明了这种关系对GL 2（D）的许多（可能所有）离散级数表示都成立.
For a division algebra D over a p-adic field F, we prove that depth is preserved under the correspondence of discrete series representations of GL n (F) and irreducible representations of D* by proving that an explicit relation holds between depth and conductor for all such representations. We also show that this relation holds for many (possibly all) discrete series representations of GL 2 (D).