Reductive Groups Dependency graph

Algebraic Groups
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AlgebraicGroups.Forms
AlgebraicGroups.Tori
abv
additive-group
adeles
adjoint
adjoint-action
adjoint-group
adjunction
admissible-sets
affine-algebraic-groups
affine-group-scheme
affine-group-schemes
affine-root-systems
affine-schemes
affine-variety
affine-weyl-groups
algebra-hom
algebraic-fundamental-group
algebraic-group
algebraic-groups
anisotropic
antipode
apartments
automorphisms
b-g
bala-carter
base-change
based-root-data
basic-elements
bd-covers
bialgebra
bn-pairs
borel
borel-subgroup
borel-subgroups
bruhat-decomposition
bruhat-order
bruhat-tits
bruhat-tits-buildings
brylinski-deligne
buildings-and-parahorics
cartan-matrices
cartan-subgroup
center
centers
central-extensions
central-isogenies
centralizer
character
character-lattice
characters
chevalley
chevalley-basis
classical-and-exceptional-groups
classical-groups
classification
closed-subgroup
closed-subgroups
coalgebra
cocharacters
cocycle
cocycles
combinatorics
commutative-algebra
commutative-group
comodule
conjugacy
connected-component
connected-components
connected-group
construction
convolution
coordinate-ring
coordinate-rings
corollary
coroot
coroots
covers
coxeter-complexes
coxeter-groups
cuspidal
decomposition
definition
definitions
deligne-lusztig
derived-group
descent
descent-and-forms
determinant
diagonalizable
diagonalizable-group
diagonalizable-groups
dual-group
dual-groups
dual-root-data
dual-root-systems
duality
dynkin-diagrams
elliptic-elements
embedding-theorem
endoscopy
equivalence
equivariant-embedding
example
examples
exceptional-groups
existence-theorem
extended-groups
external-background
f-group
f-reductive-group
f-split
f-split-torus
f-torus
facets
field-of-definition
fields
finite-field
finite-groups-lie-type
finiteness
fixed-point
formal-deformation
forms
foundational-inputs
frobenius
functor
functor-of-points
fundamental-group
g-structure
galois-action
galois-cohomology
galois-descent
galois-lattice
galois-module
general-linear-group
generated-subgroup
geometric-conjugacy
gl-v
global-fields
group-action
group-like
group-scheme
group-schemes
harish-chandra
homogeneous-space
homomorphism
hopf-algebra
hopf-algebras
hopf-spec
identity-component
images
indexed-root-datum
induced
inner-forms
integral-form
isocrystals
isogeny
isogeny-type
isomorphism-theorem
jacobson-morozov
jordan-decomposition
jordan-zassenhaus
k-theory
k2
kaletha
kernels
kottwitz
kottwitz-homomorphism
kottwitz-map
kottwitz-structures
l-groups
l-morphisms
lang-theorem
langlands
langlands-dual-groups
lemma
levi-decomposition
levi-subgroups
lie-algebra
lie-algebras
lie-kolchin
linear-algebraic-groups
local-fields
locally-closed
lusztig-series
mathlib-aligned
maximal-tori
maximal-torus
metaplectic-covers
morphisms
moy-prasad-filtrations
multiplicative-group
multiplicative-type
newton-map
nilpotent-cone
nilpotent-elements
nilpotent-orbits
nonabelian-h1
norm-one
orbit
orbital-integrals
orthogonal
outer-forms
parabolic
parabolic-subgroups
parahoric-group-schemes
parahoric-subgroups
perverse-sheaves
pinned-dual-groups
pinnings
positive-roots
pure-inner-twists
quantum-groups
quasi-split
quasi-split-forms
quasi-trivial
quotient
quotients
radical
ramification
rank
rank-one
rank-one-subgroup
rational-forms
rational-nilpotent-orbits
rational-points
rational-representation
real-forms
reductive-group
reductive-groups
reductive-quotients
reductive-structure
reflection
regular-elements
regular-semisimple
regular-unipotent
relative-root-datum
relative-weyl-group
representation
resolution
rigid-inner-forms
rigid-inner-twists
root-data
root-data-and-duality
root-data-automorphisms
root-datum
root-lattice
root-pairing
root-subgroup
root-subgroups
root-system
root-systems
roots
roots-of-unity
schubert-variety
semilinear
semisimple
semisimple-elements
semisimple-groups
semisimple-lie-algebra
sigma-conjugacy
simple-roots
simply-connected
simply-connected-cover
sl2-embedding
sl2-triples
smoothness
solvable-group
solvable-groups
spec
special-linear
special-orthogonal
speiser
spherical-buildings
split
split-rank
split-reductive-group
split-reductive-groups
split-torus
splitting-field
splittings
springer
springer-correspondence
stabilizer
stable-conjugacy
strong-inner-forms
strong-real-forms
strongly-regular
structure-constants
subtorus
symplectic
tame
tangent-space
theorem
tits-buildings
tits-index
tits-systems
tori
torsors
torus
trace-formula
triangularization
twisted-conjugacy
twisted-form
twisting
type-B
type-C
type-D
unipotent
unipotent-elements
unipotent-groups
unipotent-orbits
unipotent-radical
unipotent-radicals
unipotent-variety
unramified
valuation-rings
valued-root-data
vogan-diagrams
weakly-induced
weight-lattice
weighted-dynkin-diagrams
weil-restriction
weyl-group
weyl-groups
yoneda

Keyword: root-pairing

Definition Root Data admitted

Definition Root Systems admitted