metaplectic group
E860123
The metaplectic group is a double cover of the symplectic group that plays a central role in number theory and representation theory, particularly through its connection to theta functions and automorphic forms.
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
double cover
ⓘ
mathematical group ⓘ topological group ⓘ |
| actsOn |
Schwartz space of a symplectic vector space
ⓘ
space of theta functions ⓘ |
| arisesFrom |
Maslov index
NERFINISHED
ⓘ
square root of the determinant line bundle ⓘ |
| covers | symplectic group ⓘ |
| hasCenter | cyclic group of order 2 ⓘ |
| hasDimension | same dimension as the symplectic group ⓘ |
| hasLieAlgebra | symplectic Lie algebra ⓘ |
| hasNontrivialElementInKernelOfCoveringMap | element of order 2 GENERATED ⓘ |
| hasRepresentation |
Weil representation
NERFINISHED
ⓘ
oscillator representation ⓘ |
| isAnalogOf | spin group for the symplectic group ⓘ |
| isCentralExtensionOf | symplectic group NERFINISHED ⓘ |
| isConstructedVia |
Stone–von Neumann theorem
NERFINISHED
ⓘ
central extension of the symplectic group by μ₂ ⓘ projective representation of the symplectic group ⓘ |
| isDefinedOver |
global fields
ⓘ
local fields ⓘ p-adic fields ⓘ real numbers ⓘ |
| isDoubleCoverOf | symplectic group NERFINISHED ⓘ |
| isNontrivialCoverWhen | dimension of underlying symplectic space is at least 2 ⓘ |
| isRelatedTo |
Heisenberg group
NERFINISHED
ⓘ
Maslov class ⓘ metaplectic cover NERFINISHED ⓘ metaplectic representation ⓘ spin group NERFINISHED ⓘ |
| isUsedIn |
Fourier analysis on symplectic vector spaces
ⓘ
Langlands program NERFINISHED ⓘ Shimura correspondence NERFINISHED ⓘ Siegel modular forms ⓘ Weil representation NERFINISHED ⓘ automorphic forms ⓘ covering groups in the Langlands program ⓘ geometric quantization ⓘ half-integral weight modular forms ⓘ harmonic analysis ⓘ metaplectic forms ⓘ microlocal analysis ⓘ number theory ⓘ oscillator representation ⓘ quantization ⓘ representation theory ⓘ theory of automorphic L-functions ⓘ theta correspondence ⓘ theta functions ⓘ |
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.