百科. Langlands 对偶群 [Langlands对偶]
百科. Langlands 对偶群 [Langlands对偶]
观念
设 $G$ 为约化代数群, 其 Langlands 对偶 ${^LG}$ 是置换其根数据所得的另一个代数群.
Langlands 对应 将 $G$ (准确地说是 $G(\mathbb A_F)$) 的自守表示联系到 $^LG$-值的 Galois 表示 (即同态 $\mathrm {Gal}(\overline{F}/F)\to {^LG}$).
Langlands 对偶群也可由佐武等价定义.
性质
规范理论中的 Langlands 对偶
A gauge theory has a coupling constant $g$, which plays the role of the electric charge $e$. The conjectural non-abelian electro-magnetic duality, which has later become known as $S$-duality, has the form $(G, g) \leftrightarrow (^LG, 1/g)$.