Siegel domain
E871401
A Siegel domain is a type of complex analytic domain used in several complex variables and automorphic forms, generalizing upper half-planes to higher dimensions.
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
complex analytic domain
ⓘ
domain in several complex variables ⓘ generalization of upper half-plane ⓘ |
| appearsIn |
Langlands program
NERFINISHED
ⓘ
theory of Eisenstein series ⓘ theory of automorphic representations ⓘ theory of theta functions ⓘ |
| definedOver | complex numbers ⓘ |
| definedUsing |
Hermitian form
ⓘ
imaginary part conditions ⓘ open convex cone ⓘ |
| generalizes |
Siegel upper half-space
NERFINISHED
ⓘ
upper half-plane ⓘ |
| hasApplication |
Hodge theory
ⓘ
construction of automorphic forms ⓘ lattice counting problems ⓘ study of abelian varieties ⓘ study of moduli spaces ⓘ |
| hasCoordinateDescription | given by inequalities involving an imaginary part and a cone ⓘ |
| hasDimension | higher-dimensional complex manifold ⓘ |
| hasHistoricalDevelopment | introduced in the 20th century ⓘ |
| hasMainUse | realization of arithmetic quotients as complex manifolds ⓘ |
| hasProperty |
holomorphically convex (in typical constructions)
ⓘ
pseudoconvex (in standard settings) ⓘ |
| hasStructure | complex manifold ⓘ |
| hasType |
Siegel domain of the first kind
NERFINISHED
ⓘ
Siegel domain of the second kind ⓘ |
| namedAfter | Carl Ludwig Siegel NERFINISHED ⓘ |
| relatedConcept |
Harish-Chandra realization
NERFINISHED
ⓘ
Jordan algebra ⓘ Siegel modular variety NERFINISHED ⓘ symplectic group Sp(2g, R) NERFINISHED ⓘ tube domain ⓘ |
| relatedTo |
Hermitian symmetric space
ⓘ
bounded symmetric domain ⓘ symmetric space of non-compact type ⓘ |
| specialCase |
Siegel upper half-space of degree g
NERFINISHED
ⓘ
upper half-plane ⓘ |
| studiedIn |
analytic number theory
ⓘ
complex analysis ⓘ differential geometry ⓘ |
| usedIn |
algebraic geometry
ⓘ
arithmetic geometry ⓘ automorphic forms ⓘ representation theory ⓘ several complex variables ⓘ theory of modular forms ⓘ |
| usedToModel |
Hermitian symmetric spaces of tube type
ⓘ
certain bounded symmetric domains ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.