论文标题
在$ \ mathrm {sym}^{n} $ up $ \ mathrm {gl} _ {2} $的稳定转移中
On the Stable Transfer for $\mathrm{Sym}^{n}$ Lifting of $\mathrm{GL}_{2}$
论文作者
论文摘要
遵循\ cite {MR3117742}的范例，我们将探索$ \ mathrm {sym}^{n} $从$ \ mathrm {gl} _ {gl} _ {2} $ to $ \ mathrm {2} $ to $ \ mathrm {glmathrm {gl} n+zer non tremation fromictation notection notection notection Inder的稳定转移因子{sym}^{n} $ from in of in $ \ mathrm {gl} _ {2} $。 $ 2 $。当$ f = \ mathbb {c} $时，我们为任何$ n $构建一个明确的稳定转移因子。当$ n $很奇怪时，我们提供了一个简化的公式，将问题简化为稳定转移因子的构建，当$ l $ - 莫尔复是从$ \ mathrm {gl} _ {2} _ {2} _ {2}（\ mathbb {c}）$的对角线嵌入，以便有限多个副本$ \ m rmm {cl} c.在$ f $的残留特性的轻度假设下。有了关于残基特性的假设，还原公式在任何特征零的本地字段上都均匀地工作，除了对于$ p $ - ad的情况，我们需要排除扭曲的Steinberg表示。
Following the paradigm of \cite{MR3117742}, we are going to explore the stable transfer factors for $\mathrm{Sym}^{n}$ lifting from $\mathrm{GL}_{2}$ to $\mathrm{GL}_{n+1}$ over any local fields $F$ of characteristic zero with residue characteristic not equal to $2$. When $F=\mathbb{C}$ we construct an explicit stable transfer factor for any $n$. When $n$ is odd, we provide a reduction formula, reducing the question to the construction of the stable transfer factors when the $L$-morphism is the diagonal embedding from $\mathrm{GL}_{2}(\mathbb{C})$ to finitely many copies of $\mathrm{GL}_{2}(\mathbb{C})$ under mild assumptions on the residue characteristic of $F$. With the assumptions on the residue characteristic, the reduction formula works uniformly over any local fields of characteristic zero, except that for $p$-adic situation we need to exclude the twisted Steinberg representations.
