论文标题
$ V（ρ）$分支的注释
A note on branching of $V(ρ)$
论文作者
论文摘要
令$ \ mathfrak {g} $为一个复杂的简单谎言代数，让$ \ mathfrak {g} _0 $为$ \ mathfrak {g} $的图表自动形态固定的子algebra。让$ g $成为复杂，简单连接的，简单的代数群，带有lie代数$ \ mathfrak {g} $，让$ g_0 $为$ g $的连接子组，带有lie algebra $ \ mathfrak {g} _0 $。令$ρ$为$ \ mathfrak {g} $的正根的一半。在本文中，我们给出了最高重量$ \ mathfrak {g} _0 $ -presentation $ v_0（dμ）$的必要条件
Let $\mathfrak{g}$ be a complex simple Lie algebra and let $\mathfrak{g}_0$ be the sub-algebra fixed by a diagram automorphism of $\mathfrak{g}$. Let $G$ be the complex, simply-connected, simple algebraic group with Lie algebra $\mathfrak{g}$, and let $G_0$ be the connected subgroup of $G$ with Lie algebra $\mathfrak{g}_0$. Let $ρ$ be the half sum of positive roots of $\mathfrak{g}$. In this article, we give a necessary and sufficient condition for a highest weight $\mathfrak{g}_0$-representation $V_0(dμ)$ to occur in the representation ${\rm res}_{\mathfrak{g}_0}V(dρ)$, for any saturation factor $d$ of the pair $(G_0, G)$.
