Algebraic Groups.Root Data

Topic Automorphisms of Root Data admitted

Topic Based Root Data admitted

Theorem Bruhat Decomposition admitted

Theorem Bruhat Order Gives Schubert Closure Relations admitted

Topic Cartan Matrices and Dynkin Diagrams admitted

Topic Centers and Dual Centers admitted

Topic Central Isogenies and Duality admitted

Definition Chevalley Basis admitted

Theorem Chevalley Existence Theorem admitted

Definition Chevalley Group Construction from a Root Datum admitted

Theorem Chevalley Isomorphism Theorem admitted

Theorem Chevalley Isomorphism Theorem for F-Split Groups admitted

Theorem Classification of Irreducible Root Systems admitted

Topic Classification of Split Reductive Groups admitted

Topic Coxeter Systems and Bruhat Order admitted

Definition Crystallographic and Reduced Root Systems admitted

Theorem Diagonalizable Groups Are Dual to Character Groups admitted

Topic Dual Reductive Groups admitted

Topic Dual Root Data admitted

Topic Dual Root Systems admitted

Topic Fundamental Group of a Root Datum admitted

Topic Galois Action on Root Data admitted

Definition Indexed Root Datum of an F-Reductive Group admitted

Definition Isogeny Types from the Root Datum admitted

Topic L-Groups admitted

Topic L-Morphisms admitted

Topic Langlands Dual Groups admitted

Theorem Levi Decomposition of Parabolic Subgroups admitted

Topic Pinned Dual Groups admitted

Topic Pinnings admitted

Theorem Quasi-Split and Anisotropic Groups via the Indexed Root Datum admitted

Definition Rank-One Subgroups and SL₂-Embeddings admitted

Theorem Rational Bruhat Decomposition admitted

Theorem Relative Root Datum of an F-Reductive Group admitted

Theorem Relative Weyl Group Is Generated by Relative Reflections admitted

Theorem Root Chains and the String Property admitted

Definition Root Data admitted

Definition Root Datum of a Reductive Group admitted

Theorem Root Form and Positive Definiteness admitted

Definition Root Pairings (Unified Framework) admitted

Theorem Root Subgroups Generate a Reductive Group admitted

Definition Root Systems admitted

Topic Roots, Coroots, and Root Subgroups admitted

Definition Split Reductive Groups admitted

Theorem Standard Parabolics Are Classified by Simple Roots admitted

Theorem Unipotent Radical of a Borel Subgroup and Positive Roots admitted

Theorem Weyl Group Is Generated by Root Reflections admitted

Topic Weyl Groups admitted

Theorem Weyl Groups as Coxeter Groups admitted