# Abelian ideals of a Borel subalgebra and root systems

Journal of the European Mathematical Society (2014)

- Volume: 016, Issue: 12, page 2693-2708
- ISSN: 1435-9855

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topPanyushev, 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 -

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