论文标题
广义线性周期
The generalized linear period
论文作者
论文摘要
令$ f $为特征零的非一切本本地字段。我们研究了这对$（g，h_ {p，p+1}）的线性周期问题=（gl_ {2p+1}（f），gl_ {p}（p}（f）\ times gl_ {p+1}（f））$当μ是一个好角色时。我们还表明，任何$ p \ cap h_ {p，p+1} $ - 在$ h_ {p，p，p+1} $上函数在$ h_ {p，p+1} $上 - $ g $的不可差的平滑表示$ g $也是$ h_ {p，p，p+1} $ - 当$ p $是$ p $的$ p $是$ p $的$ p $ $ p $ $ g $ g $ g $ g $ $（0，\ cdots，0,1）$。
Let $F$ be a non-archimedean local field of characteristic zero. We study the linear period problem for the pair $(G,H_{p,p+1})=(GL_{2p+1}(F), GL_{p}(F)\times GL_{p+1}(F))$ and we prove that any bi-$(H_{p,p+1},μ)$-invariant generalized function on $G$ is invariant under the matrix transpose when μis a good character. We also show that any $P\cap H_{p,p+1}$-invariant linear functional on an $H_{p,p+1}$-distinguished irreducible smooth representation of $G$ is also $H_{p,p+1}$-invariant when F is nonarchimedean, where $P$ is a standard mirabolic subgroup of $G$ with last row vector $(0,\cdots,0,1)$.
