论文标题
$ \ mathrm {gl} _n $的gelfand-kirillov维度
Gelfand-Kirillov dimension of representations of $\mathrm{GL}_n$ over a non-archimedean local field
论文作者
论文摘要
我们计算$π$的固定矢量的渐近行为相对于紧凑型开放子组$ 1+ m_n（\ mathfrak {p}^n）\ subset \ subset \ mathrm {gl} _n（gl} _n _n（f）$ $π$的$ \ mathrm a n n n n n n n n n n n n n n n n n n n n n n n n n n and and and} 场地。这样的尺寸可以通过$π$的特征的细菌来计算。我们还对这些维度在Langlands功能的实例中的行为如何（例如Jacquet-Langlands对应关系和循环基础变化）进行了一些观察。
We calculate the asymptotic behavior of the dimension of the fixed vectors of $π$ with respect to compact open subgroups $1+ M_n(\mathfrak{p}^N)\subset\mathrm{GL}_n(F)$ for $π$ an admissible representation of $\mathrm{GL}_n(F)$, and $F$ a nonarchimedean local field. Such dimensions can be calculated by germs of the character of $π$. We also make some observations on how those dimensions behave under instances of Langlands functoriality, such as the Jacquet-Langlands correspondence and cyclic base change, where relations between characters are known.
