论文标题
有限组的对称对的多个界限
Bounds on multiplicities of symmetric pairs of finite groups
论文作者
论文摘要
令$γ$为有限的组，让$θ$成为$γ$的互动，让$ρ$是$γ$的不可约复合代表。我们限制了$ \ dimρ^{γ^θ} $，根据忠实的$ \ m athbb {f} _p $ -presentation $γ/rad_p（γ）$的最小维度，其中$ p $是任何奇数prime prime和$ rad_p（γ）$是$ p $ p $ p $ - $ - $ - $ - $ -SUB-subgroups $ a $ subgump， 这特别是意味着，如果$ \ mathbf {g} $是$ \ mathbb {z} $上的组方案，而$θ$是$ \ mathbf {g} $的互动，那么在$ c^\ infty \ weft（\ mathbf}/ zbb {z^zp）中，任何不可约的表示\ Mathbf {g} ^θ（\ Mathbb {z} _p）\ right）$是限制的，在$ p $中均匀。
Let $Γ$ be a finite group, let $θ$ be an involution of $Γ$, and let $ρ$ be an irreducible complex representation of $Γ$. We bound $\dim ρ^{Γ^θ}$ in terms of the smallest dimension of a faithful $\mathbb{F}_p$-representation of $Γ/Rad_p(Γ)$, where $p$ is any odd prime and $Rad_p(Γ)$ is the maximal normal $p$-subgroup of $Γ$. This implies, in particular, that if $\mathbf{G}$ is a group scheme over $\mathbb{Z}$ and $θ$ is an involution of $\mathbf{G}$, then the multiplicity of any irreducible representation in $C^\infty \left( \mathbf{G}(\mathbb{Z}_p)/ \mathbf{G} ^θ(\mathbb{Z}_p) \right)$ is bounded, uniformly in $p$.
