I am looking for a good (textbook) reference for the basic fact (due to Chevalley) that for every semisimple Lie group $G$ (without compact factors) with Weyl group $W$, the Bruhat order on $W$ coincides with the inclusion order between Schubert cycles in flag-manifolds of $G$. Sadly, the only reference I know is the original Chevalley's paper ("Sur les decompositions cellulaires des espaces $G/B$") published in 1994 (but written in 1950s). Note, I am not looking for a proof (I know how to prove it), just for a reference. Yes, I am looking at the groups which do not necessarily split (the proof I know covers such groups).
Bruhat order and Schubert cycles
Misha
- 31.2k
- 1
- 94
- 163