Abstract
Let 𝔤 be a simple Lie algebra with a Borel subalgebra 𝔟 and 𝔄𝔟 the set of abelian ideals of 𝔟. Let Δ+ be the corresponding set of positive roots. We continue our study of combinatorial properties of the partition of 𝔄𝔟 parameterised by the long positive roots. In particular, the union of an arbitrary set of maximal abelian ideals is described, if 𝔤 ≠𝔰𝔩n. We also characterise the greatest lower bound of two positive roots, when it exists, and point out interesting subposets of Δ+ that are modular lattices.
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Acknowledgements
Part of this work was done during my stay at the Max-Planck-Institut fĂĽr Mathematik (Bonn). I would like to thank the Institute for its warm hospitality and excellent working conditions.
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Presented by: Michel Brion
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This research is partially supported by the R.F.B.R. grant N0 16-01-00818.
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Panyushev, D.I. Abelian Ideals of a Borel Subalgebra and Root Systems, II. Algebr Represent Theor 23, 1487–1498 (2020). https://doi.org/10.1007/s10468-019-09902-7
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DOI: https://doi.org/10.1007/s10468-019-09902-7