格余体积与离散级数形式维数的乘积：p-adic GL（2）
The product of lattice covolume and discrete series formal dimension: p-adic GL(2)
摘要：
设$F$是特征为$0$的非阿基米德局部域，剩余域的阶不能被$2$整除.我们展示了如何计算的产品的无挠晶格在$PGL(2,F)$和形式尺寸的离散系列表示的$GL(2,F)$的共同体积。余体积来自伊原的一个定理，形式维数包含在Corwin，Moy和Sally的结果中。由一个定理回到阿蒂亚，并由平凡的第二上同调群的自由群，所产生的产品是冯诺依曼维数的离散系列表示被视为代表的自由群的因素。
英文摘要：
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 $PGL(2,F)$ and the formal dimension of a discrete series representation of $GL(2,F)$. 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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