Combinatorial and Geometric Constructions Associated with the Kostant Cascade
Journal of Lie Theory, Volume 33 (2023) no. 2, pp. 497-526
Let $\mathfrak g$ be a complex simple Lie algebra and $\mathfrak b=\mathfrak t\oplus\mathfrak u^+$ a fixed Borel subalgebra. Let $\Delta^+$ be the set of positive roots associated with $\mathfrak u^+$ and $\mathfrak gK\subset\Delta^+$ the Kostant cascade. We elaborate on some constructions related to $\mathfrak gK$ and applications of $\mathfrak gK$. This includes the cascade element $x_\mathfrak gK$ in the Cartan subalgebra $\mathfrak t$ and properties of certain objects naturally associated with $\mathfrak gK$: an abelian ideal of $\mathfrak b$, a nilpotent $G$-orbit in $\mathfrak g$, and an involution of $\mathfrak g$.
@article{JOLT_2023_33_2_a2,
author = {D. I. Panyushev},
title = {Combinatorial and {Geometric} {Constructions} {Associated} with the {Kostant} {Cascade
}},
journal = {Journal of Lie Theory},
pages = {497--526},
year = {2023},
volume = {33},
number = {2},
doi = {10.5802/jolt.1292},
zbl = {1527.17005},
language = {en},
url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1292/}
}
TY - JOUR AU - D. I. Panyushev TI - Combinatorial and Geometric Constructions Associated with the Kostant Cascade JO - Journal of Lie Theory PY - 2023 SP - 497 EP - 526 VL - 33 IS - 2 UR - https://jolt.centre-mersenne.org/articles/10.5802/jolt.1292/ DO - 10.5802/jolt.1292 LA - en ID - JOLT_2023_33_2_a2 ER -
D. I. Panyushev. Combinatorial and Geometric Constructions Associated with the Kostant Cascade. Journal of Lie Theory, Volume 33 (2023) no. 2, pp. 497-526. doi: 10.5802/jolt.1292
Cited by Sources: