Faculty Publications
Conjugates Of Rational Equivariant Holomorphic Maps Of Symmetric Domains
Document Type
Article
Keywords
Equivariant holomorphic maps, Hermitian symmetric domains, Kuga fiber varieties, Locally symmetric spaces
Journal/Book/Conference Title
Monatshefte fur Mathematik
Volume
141
Issue
3
First Page
187
Last Page
196
Abstract
Let τ : script D sign → script D sign′ be an equivariant holomorphic map of symmetric domains associated to a homomorphism ρ : double-struct G sign → double-struct G sign′ of semisimple algebraic groups defined over ℚ. If Γ ⊂ double-struct G sign (ℚ) and Γ′ ⊂ double-struct G sign′(ℚ) are torsion-free arithmetic subgroups with ρ (Γ)⊂ Γ′, the map τ induces a morphism φ: Γ/script D sign → Γ′/script D sign′ of arithmetic varieties and the rationality of τ is defined by using symmetries on script D sign and script D sign′ as well as the commensurability groups of Γ and Γ′. An element σ ∈ Aut(ℂ) determines a conjugate equivariant holomorphic map τσ : script D sign;σ → script D sign′σ of τ which induces the conjugate morphism φσ : (Γ/script D sign)σ → (Γ′/script D sign′)σ of φ. We prove that τσ is rational if τ is rational.
Department
Department of Mathematics
Original Publication Date
1-1-2004
DOI of published version
10.1007/s00605-003-0196-1
Recommended Citation
Lee, Min Ho, "Conjugates Of Rational Equivariant Holomorphic Maps Of Symmetric Domains" (2004). Faculty Publications. 3183.
https://scholarworks.uni.edu/facpub/3183
