格协体积与离散级数形式维数的乘积:p进GL(2)

IF 0.8 4区数学 Q2 MATHEMATICS

Expositiones Mathematicae Pub Date : 2023-03-01 DOI:10.1016/j.exmath.2022.09.001

L.C. Ruth

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引用次数: 0

摘要

设F为特征为0的非阿基米德局部域和不能被2整除的阶剩余域。我们展示了如何计算PGL(2,F)中无扭转晶格的协体积与GL(2,F)的离散级数表示的形式维数的乘积。协体积来自Ihara的一个定理，形式维数包含在Corwin、Moy和Sally的结果中。通过一个可以追溯到Atiyah的定理，以及一个自由群的第二个上同调群的平凡性，得到的乘积是一个离散级数表示的冯·诺依曼维，被认为是一个自由群因子的表示。

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The product of lattice covolume and discrete series formal dimension: p-adic GL(2)

Let $F$ be a nonarchimedean local field of characteristic 0 and residue field of order not divisible by 2. We show how to calculate the product of the covolume of a torsion-free lattice in $P G L (2, F)$ and the formal dimension of a discrete series representation of $G L (2, F)$ . The covolume comes from a theorem of Ihara, and the formal dimensions are contained in results of Corwin, Moy, and Sally. By a theorem going back to Atiyah, and by triviality of the second cohomology group of a free group, the resulting product is the von Neumann dimension of a discrete series representation considered as a representation of a free group factor.

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来源期刊

Expositiones Mathematicae 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

40 days

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