论文标题
还原组的缠绕字符公式
The twining character formula for reductive groups
论文作者
论文摘要
令$ \ wideHat {g} $成为一个连接的还原组，在代数封闭的字段上具有固定的外部自动形态$σ$。詹森（Jantzen）的缠绕角色公式将$σ$的动作痕迹与最高重量表示的$v_μ$的$ \ \ widehat {g} $相关的痕迹与相应的最高重量表示表示$（v_σ）_μ$的角色相关的相关组$ \ wideHat $ \ wideHat {g^{g^{c pick，c pick，c pick，v_σ）_ $。本文扩展了Hong $ \ wideHat {g} $的几何形状证明的方法，以证明该公式为所有连接的还原组都保留，并检查了其他假设的作用。在最后一部分中，解释了如何使用这些结果来在非Archimedean本地领域中得出有关准分组的结论。因此，本文提供了更通用的几何证据，证明了Jantzen缠绕角色公式，并在此过程中提供了一些独立兴趣的新结果。
Let $\widehat{G}$ be a connected reductive group over an algebraically closed field with a pinning-preserving outer automorphism $σ$. Jantzen's twining character formula relates the trace of the action of $σ$ on a highest-weight representation $V_μ$ of $\widehat{G}$ to the character of a corresponding highest-weight representation $(V_σ)_μ$ of a related group $\widehat{G^{σ, \circ}}$. This paper extends the methods of Hong's geometric proof for the case $\widehat{G}$ is adjoint, to prove that the formula holds for all connected reductive groups, and examines the role of additional hypotheses. In the final section, it is explained how these results can be used to draw conclusions about quasi-split groups over a non-Archimedean local field. This paper thus provides a more general geometric proof of the Jantzen twining character formula and provides some apparently new results of independent interest along the way.
