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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Abelian ideals and cohomology of symplectic type


Author: Li Luo
Journal: Proc. Amer. Math. Soc. 137 (2009), 479-485
MSC (2000): Primary 17B05, 17B56; Secondary 17B20, 17B30
DOI: https://doi.org/10.1090/S0002-9939-08-09685-8
Published electronically: September 29, 2008
MathSciNet review: 2448567
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Abstract: Let $\mathfrak {b}$ be a Borel subalgebra of the symplectic Lie algebra $\mathfrak {sp}(2n,\mathbb {C})$ and let $\mathfrak {n}$ be the corresponding maximal nilpotent subalgebra. We find a connection between the abelian ideals of $\mathfrak {b}$ and the cohomology of $\mathfrak {n}$ with trivial coefficients. Using this connection, we are able to enumerate the number of abelian ideals of $\mathfrak {b}$ with given dimension via the Poincaré polynomials of Weyl groups of types $A_{n-1}$ and $C_n$.


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Additional Information

Li Luo
Affiliation: Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
Email: luoli@amss.ac.cn

Keywords: Abelian ideal, cohomology, symplectic Lie algebra, Weyl group, Poincaré polynomial.
Received by editor(s): January 24, 2008
Published electronically: September 29, 2008
Communicated by: Gail R. Letzter
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.