Corpus ID: 119330855

Equivalence of Demazure and Bott-Samelson Resolutions via Factorization

  title={Equivalence of Demazure and Bott-Samelson Resolutions via Factorization},
  author={A. Caine},
  journal={arXiv: Differential Geometry},
  • A. Caine
  • Published 28 February 2015
  • Mathematics
  • arXiv: Differential Geometry
Let $G$, $B$, and $H$ denote a complex semi-simple algebraic group, a Borel subgroup of $G$, and a maximal complex torus in $B$, respectively. Choose a compact real form $K$ of $G$ such that $T=K\cap H$ is a maximal torus in $T$. Then there are two models for the flag space of $G$: the complex quotient $X=G/B$ and the real quotient $K/T$. These models are smoothly equivalent via the map $\tilde{\mathbf k}\colon G/B\to K/T$ induced by factorization in $G$ relative to the Iwasawa decomposition $G… Expand


Coordinates on Schubert cells, Kostant's harmonic forms, and the Bruhat Poisson structure onG/B
For the flag manifoldX=G/B of a complex semi-simple Lie groupG, we make connections between the Kostant harmonic forms onG/B and the geometry of the Bruhat Poisson structure. We show that on eachExpand
Désingularisation des variétés de Schubert généralisées
© Gauthier-Villars (Editions scientifiques et medicales Elsevier), 1974, tous droits reserves. L’acces aux archives de la revue « Annales scientifiques de l’E.N.S. » (http://www.Expand