Automorphic forms on symmetric domains of type IV

摘要

A symmetric domain of type IV is defined to be a Hermitian symmetric space l_n x O_n ), with O_(2,n)~+ the subgroup of index two singled out in the pseudo-orthogonal group O_(2,n) by the condition that the upper left minor of order two is positive. Such a domain is modelled by a domain on a quadric in the projectivization of the (n + 2)-dimensional complex vector space, on which the group O_(2,n) acts in a natural way. This defines an O_(2,n)~+-equivariant line bundle π:ψ_n→l_n (whose nth power is the canonical bundle).