This text presents topics in a systematic fashion to engage a wide readership. It includes: generalities on G/B and G/Q; the Grassmannian and the flag variety S... » 

This text presents topics in a systematic fashion to engage a wide readership. It includes: generalities on G/B and G/Q; the Grassmannian and the flag variety SL_n/B' the tangent space and smoothness; rational smoothness and Kazhdan-Lusztig theory; and root system description of T (w,/tau). «