|
gptkbp:instanceOf
|
gptkb:Lie_group
|
|
gptkbp:alsoKnownAs
|
orthogonal group
|
|
gptkbp:appearsIn
|
gptkb:algebraic_geometry
number theory
quantum mechanics
|
|
gptkbp:centralTo
|
{±I}
|
|
gptkbp:compact
|
gptkb:compact_symplectic_group
|
|
gptkbp:complexForm
|
gptkb:Sp(2n,_C)
|
|
gptkbp:connects
|
true
|
|
gptkbp:definedIn
|
gptkb:Field
|
|
gptkbp:dimensions
|
n(2n+1)
|
|
gptkbp:hasSubgroup
|
GL(2n)
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
Sp(2n)
|
|
gptkbp:isSimple
|
n > 1
|
|
gptkbp:notation
|
gptkb:Sp(2n,_F)
Sp_{2n}
|
|
gptkbp:preserves
|
symplectic form
|
|
gptkbp:rank
|
n
|
|
gptkbp:realForm
|
gptkb:Sp(2n,_R)
|
|
gptkbp:relatedGroup
|
gptkb:Sp(2n,_C)
gptkb:USp(2n)
gptkb:Sp(2n,_R)
Sp(2n, F_q)
Sp(2n, Q)
Sp(2n, Z)
PSp(2n)
|
|
gptkbp:relatedTo
|
gptkb:general_linear_group
gptkb:Hamiltonian_mechanics
gptkb:Siegel_modular_group
modular forms
representation theory
Cartan subalgebra
algebraic groups
automorphic forms
orthogonal group
symplectic geometry
Galois representations
theta functions
unitary representations
classical groups
symplectic matrices
Dynkin diagram of type C_n
Weyl group of type C_n
|
|
gptkbp:simplyConnected
|
true
|
|
gptkbp:type
|
gptkb:group_of_people
gptkb:C_n
classical group
|
|
gptkbp:bfsParent
|
gptkb:Lie_type_C_n
|
|
gptkbp:bfsLayer
|
8
|