论文标题
在伴骨的borel subonoid上
On the Borel Submonoid of a Symplectic Monoid
论文作者
论文摘要
在本文中，我们研究了复杂的符号单体$ MSP_N $的Bruhat-Chevalley-Renner订单。在证明该订单完全由Bruhat-chevalley-Renner订单确定，在$ n \ times n $矩阵$ m_n $的线性代数单体上，我们专注于$ MSP_N $的Borel submonoid。通过使用此下monoid，我们引入了一组新的B类设置分区。我们通过使用``折叠''和``展开''操作员来确定他们的计数。我们表明，合理平滑还原性单体零的Borel亚monoid在理性上是平滑的。最后，我们分析了$ m_n $和$ msp_n $的Borel半群的Nilpotent子群。我们表明，与$ MSP_N $的情况相反，$ m_n $的borel submonoid的nilpotent子群是不可约的。
In this article, we study the Bruhat-Chevalley-Renner order on the complex symplectic monoid $MSp_n$. After showing that this order is completely determined by the Bruhat-Chevalley-Renner order on the linear algebraic monoid of $n\times n$ matrices $M_n$, we focus on the Borel submonoid of $MSp_n$. By using this submonoid, we introduce a new set of type B set partitions. We determine their count by using the ``folding'' and ``unfolding'' operators that we introduce. We show that the Borel submonoid of a rationally smooth reductive monoid with zero is rationally smooth. Finally, we analyze the nilpotent subsemigroups of the Borel semigroups of $M_n$ and $MSp_n$. We show that, contrary to the case of $MSp_n$, the nilpotent subsemigroup of the Borel submonoid of $M_n$ is irreducible.
