Abelian ideals of a Borel subalgebra and root systems

Panyushev, Dmitri I.. "Abelian ideals of a Borel subalgebra and root systems." Journal of the European Mathematical Society 016.12 (2014): 2693-2708. <http://eudml.org/doc/277536>.

@article{Panyushev2014,
abstract = {Let $\mathfrak \{g\}$ be a simple Lie algebra and $\mathfrak \{Ab\}^o$ the poset of non-trivial abelian ideals of a fixed Borel subalgebra of $\mathfrak \{g\}$. In [8], we constructed a partition $\mathfrak \{Ab\}^o =\sqcup _\mu \mathfrak \{Ab\}_\mu $ parameterised by the long positive roots of $\mathfrak \{g\}$ and studied the subposets $\mathfrak \{Ab\}_\mu $. In this note, we show that this partition is compatible with intersections, relate it to the Kostant-Peterson parameterisation and to the centralisers of abelian ideals. We also prove that the poset of positive roots of $\mathfrak \{g\}$ is a join-semilattice.},
author = {Panyushev, Dmitri I.},
journal = {Journal of the European Mathematical Society},
keywords = {root system; Borel subalgebra; minuscule element; abelian ideal; root system; Borel subalgebra; minuscule element; abelian ideal},
language = {eng},
number = {12},
pages = {2693-2708},
publisher = {European Mathematical Society Publishing House},
title = {Abelian ideals of a Borel subalgebra and root systems},
url = {http://eudml.org/doc/277536},
volume = {016},
year = {2014},
}

TY - JOUR
AU - Panyushev, Dmitri I.
TI - Abelian ideals of a Borel subalgebra and root systems
JO - Journal of the European Mathematical Society
PY - 2014
PB - European Mathematical Society Publishing House
VL - 016
IS - 12
SP - 2693
EP - 2708
AB - Let $\mathfrak {g}$ be a simple Lie algebra and $\mathfrak {Ab}^o$ the poset of non-trivial abelian ideals of a fixed Borel subalgebra of $\mathfrak {g}$. In [8], we constructed a partition $\mathfrak {Ab}^o =\sqcup _\mu \mathfrak {Ab}_\mu $ parameterised by the long positive roots of $\mathfrak {g}$ and studied the subposets $\mathfrak {Ab}_\mu $. In this note, we show that this partition is compatible with intersections, relate it to the Kostant-Peterson parameterisation and to the centralisers of abelian ideals. We also prove that the poset of positive roots of $\mathfrak {g}$ is a join-semilattice.
LA - eng
KW - root system; Borel subalgebra; minuscule element; abelian ideal; root system; Borel subalgebra; minuscule element; abelian ideal
UR - http://eudml.org/doc/277536
ER -