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- W2246030817 abstract "Let $frb$ be a fixed Borel subalgebra of a finite-dimensional complex simple Lie algebra $frg$. The Shi bijection associates to every ad-nilpotent ideal $fri$ of $frb$ a region $V_{fri}$. In this paper, we show that $fri$ is abelian if and only if $V_{fri}cap 2A$ is empty, if and only if the volume of $V_{fri}cap 2A$ equals to that of $A$, where $A$ is the fundamental alcove of the affine Weyl group. For certain flag of abelian ideals, we record an ascending property of their associated regions. We also determine the maximal eigenvalue $m_{r-1}$ of the Casimir operator on $wedge^{r-1} frg$ and the corresponding eigenspace $M_{r-1}$, where $r$ is the number of positive roots." @default.
- W2246030817 created "2016-06-24" @default.
- W2246030817 creator A5049207611 @default.
- W2246030817 date "2013-08-20" @default.
- W2246030817 modified "2023-09-26" @default.
- W2246030817 title "Remarks on the abelian ideals of a Borel subalgebra" @default.
- W2246030817 doi "https://doi.org/10.48550/arxiv.1308.4464" @default.
- W2246030817 hasPublicationYear "2013" @default.
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