Combinatorial analogues of ad-nilpotent ideals for untwisted affine Lie   algebras
  We study certain types of ideals in the standard Borel subalgebra of an untwisted affine Lie algebra. We classify these ideals in terms of the root combinatorics and give an explicit formula for the number of such ideals in type $A$. The formula involves various aspects of combinatorics of Dyck paths and leads to a new interesting integral sequence. 
Karin Baur and Volodymyr Mazorchuk
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