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Enumeration of Basic Ideals in Type ***B* Lie Algebras

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Jonathan Nilsson

Department of Mathematics

Uppsala University

P. O. Box 480

SE-751 06, Uppsala

Sweden

**Abstract:**

The number of ad-nilpotent ideals of the Borel subalgebra of the
classical Lie algebra of type *B*_{n} 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 *B*_{n}, 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 *B*_{n}, 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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