Parabolic contractions of semisimple Lie algebras and their invariants

@article{Panyushev2013ParabolicCO,
  title={Parabolic contractions of semisimple Lie algebras and their invariants},
  author={Dmitri I. Panyushev and Oksana Sergeevna Yakimova},
  journal={Selecta Mathematica},
  year={2013},
  volume={19},
  pages={699-717}
}
  • Dmitri I. Panyushev, Oksana Sergeevna Yakimova
  • Published 2013
  • Mathematics
  • Selecta Mathematica
  • Let $$G$$ be a connected semisimple algebraic group with Lie algebra $$\mathfrak{g }$$ and $$P$$ a parabolic subgroup of $$G$$ with $$\mathrm{Lie\, }P=\mathfrak{p }$$. The parabolic contraction $$\mathfrak{q }$$ of $$\mathfrak{g }$$ is the semi-direct product of $$\mathfrak{p }$$ and a $$\mathfrak{p }$$-module $$\mathfrak{g }/\mathfrak{p }$$ regarded as an abelian ideal. We are interested in the polynomial invariants of the adjoint and coadjoint representations of $$\mathfrak{q }$$. In the… CONTINUE READING