Abelian Ideals and Cohomology of Symplectic Type

Details Abelian Ideals and Cohomology of Symplectic Type Abelian Ideals and Cohomology of Symplectic Type

2008-04-08

arxiv.org/abs/0804.1264v1

Mathematics

Rings and Algebras

6 pages

Scientific paper

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 $C_n$.

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