Subvarieties of quotients of bounded symmetric domains

Modular subvarieties of arithmetic quotients of bounded symmetric domains

A reductive Q-simple algebraic group G is of hermitian type, if the symmetric space D defined by G(R) is a hermitian symmetric space. A discrete subgroup Γ ⊂ G(Q) is arithmetic, if for some faithful rational representation ρ : G −→ GL(V ), and for some lattice VZ ⊂ VQ, Γ is commensurable with ρ−1(GL(VZ)). A non-compact hermitian symmetric space is holomorphically equivalent to a bounded symmetr...

On the Compactification of Arithmetically Defined Quotients of Bounded Symmetric Domains

In previous papers [13], [2], [16], [3], [ l l ] , the theory of automorphic functions for some classical discontinuous groups F, such as the Siegel or Hilbert-Siegel modular groups, acting on certain bounded symmetric domains X, has been developed through the construction of a natural compactification of X/T , which is a normal analytic space, projectively embeddable by means of automorphic fo...

Bounded Holomorphic Functions on Bounded Symmetric Domains

Let D be a bounded homogeneous domain in C , and let A denote the open unit disk. If z e D and /: D —► A is holomorphic, then ß/(z) is defined as the maximum ratio \Vz(f)x\/Hz(x, 3c)1/2 , where x is a nonzero vector in C and Hz is the Bergman metric on D . The number ßf(z) represents the maximum dilation of / at z . The set consisting of all ß/(z), for z e D and /: D —► A holomorphic, is known ...

Bloch Constants of Bounded Symmetric Domains

Let D1 and D2 be two irreducible bounded symmetric domains in the complex spaces V1 and V2 respectively. Let E be the Euclidean metric on V2 and h the Bergman metric on V1. The Bloch constant b(D1,D2) is defined to be the supremum of E(f ′(z)x, f ′(z)x) 1 2 /hz(x, x)1/2, taken over all the holomorphic functions f : D1 → D2 and z ∈ D1, and nonzero vectors x ∈ V1. We find the constants for all th...

Generalized Cayley Transformations of Bounded Symmetric Domains