海藻李代数中A型双元和Richardson元的例外表示
Exceptional representations of a double quiver of type A, and Richardson elements in seaweed Lie algebras
摘要：
本文研究了由$A$型箭图的二重子产生的拟遗传代数的$Δ$ -滤模集.我们的主要结果是，对于任何固定的$Δ$ -维数向量，有一个唯一的（同构）例外$Δ$ -过滤模块。然后，我们应用这个结果证明了在$\mathrm{gl}_{n}(\field)$中的海藻李代数的幂零根上总是存在一个开伴随轨道，从而在这个$\mathrm{gl}_{n}(\field)$例子中肯定地回答了Michel Duflo和Dmitri Panyushev独立提出的一个问题.给出了$E_{8}$型单李代数中的海藻李代数在其幂零根上不允许有开轨的一个例子。
英文摘要：
In this paper, we study the set of $Δ$-filtered modules of quasi-hereditary algebras arising from quotients of the double of quivers of type $A$. Our main result is that for any fixed $Δ$-dimension vector, there is a unique (up to isomorphism) exceptional $Δ$-filtered module. We then apply this result to show that there is always an open adjoint orbit in the nilpotent radical of a seaweed Lie algebra in $\mathrm{gl}_{n}(\field)$, thus answering positively in this $\mathrm{gl}_{n}(\field)$ case to a question raised independently by Michel Duflo and Dmitri Panyushev. An example of a seaweed Lie algebra in a simple Lie algebra of type $E_{8}$ not admitting an open orbit in its nilpotent radical is given.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
