Algebraic groups and related topics:

abelian action affine Weyl group algebraic group algebraic operations assume automorphism bijection birational Borel subgroup Cartan Cartan subalgebras character closure codimension cohomology commutative component conjugacy class consider coordinate Corollary cuspidal decomposition defined definition denote diagram dimension exact sequence exists a morphism fibre finite follows formula function G is contained given Hence highest weight homogeneous induced integer invariant irreducible representation isomorphic left cells Lemma Let G Lie algebra line bundle linear Lusztig Math maximal torus module Moreover morphism nilpotent element non-zero notation obtained open orbit open set parabolic subgroup partition PGL2 polynomial Proof Proposition prove rank regular configuration resp result root system satisfying semisimple SL2-module Springer correspondence subgroup of G subset subspace subvariety symmetric pair Theorem 2.2 torus embedding triplet trivial Umemura U3 unipotent classes unipotent radical unique variety vector space