Abelian Ideals and Cohomology of Symplectic Type
Abelian Ideals and Cohomology of Symplectic Type
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DOI：
10.1090/s0002-9939-08-09685-8
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发表时间：
2008-04
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影响因子：
--
通讯作者：
Lipeng Luo
中科院分区：
文献类型：
--
作者：
Lipeng Luo
For symplectic Lie algebras $\mathfrak{sp}(2n,\mathbb{C})$, denote by $\mathfrak{b}$ and $\mathfrak{n}$ its Borel subalgebra and maximal nilpotent subalgebra, respectively. We construct a relationship between the abelian ideals of $\mathfrak{b}$ and the cohomology of $\mathfrak{n}$ with trivial coefficients. By this relationship, we can enumerate the number of abelian ideals of $\mathfrak{b}$ with certain dimension via the Poincare polynomials of Weyl groups of type $A_{n-1}$ and $C_n$.
