Abstract
Let \(\mathfrak {g}\) be a complex simple Lie algebra. We classify the parabolic subalgebras \(\mathfrak {p}\) of \(\mathfrak {g}\) such that the nilradical of \(\mathfrak {p}\) has a commutative polarisation. The answer is given in terms of the Kostant cascade. It requires also the notion of an optimal nilradical and some properties of abelian ideals in a Borel subalgebra of \(\mathfrak {g}\).
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Presented by: Michel Brion
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To my friend and colleague Alexander G. Elashvili, with gratitude
This research was funded by RFBR, project No. 20-01-00515.
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Panyushev, D.I. Commutative Polarisations and the Kostant Cascade. Algebr Represent Theor 26, 967–985 (2023). https://doi.org/10.1007/s10468-022-10118-5
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DOI: https://doi.org/10.1007/s10468-022-10118-5