Journal of Integer Sequences, Vol. 15 (2012), Article 12.9.5

Enumeration of Basic Ideals in Type B Lie Algebras

Jonathan Nilsson
Department of Mathematics
Uppsala University
P. O. Box 480
SE-751 06, Uppsala


The number of ad-nilpotent ideals of the Borel subalgebra of the classical Lie algebra of type Bn is determined using combinatorial arguments involving a generalization of Dyck-paths. We also solve a similar problem for the untwisted affine Lie algebra of type Bn, where we instead enumerate a certain class of ideals called basic ideals. This leads to an explicit formula for the number of basic ideals in Bn, which gives rise to a new integer sequence.

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Received April 17 2012; revised versions received August 15 2012; November 17 2012. Published in Journal of Integer Sequences, November 20 2012.

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