A型Frobenius海藻的完整光谱
The unbroken spectrum of type-A Frobenius seaweeds
摘要：
若$\mathfrak{g}$是Frobenius李代数，则对一定的$F\in \mathfrak{g}^*$，由$x \longmapsto F[x,-]$给出的自然映射$\mathfrak{g}\longrightarrow \mathfrak{g}^* $是同构.在这种同构下的$F$的逆像称为主元素。证明了如果$\mathfrak{g}$是$A_{n-1}=\mathfrak{sl}(n)$的Frobenius海藻子代数，则主元伴随的谱由整数的连续集组成，其重数具有对称分布.我们的证明方法是建设性的和组合的性质。
英文摘要：
If $\mathfrak{g}$ is a Frobenius Lie algebra, then for certain $F\in \mathfrak{g}^*$ the natural map $\mathfrak{g}\longrightarrow \mathfrak{g}^* $ given by $x \longmapsto F[x,-]$ is an isomorphism. The inverse image of $F$ under this isomorphism is called a principal element. We show that if $\mathfrak{g}$ is a Frobenius seaweed subalgebra of $A_{n-1}=\mathfrak{sl}(n)$ then the spectrum of the adjoint of a principal element consists of an unbroken set of integers whose multiplicities have a symmetric distribution. Our proof methods are constructive and combinatorial in nature.
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