Let
K = quadratic imaginary extension of Q
V = rank n K-vector space with a Hermitian form of signature (n-1,1)
U = U(V) the associated unitary group
By a holomorphic automorphic form for U of weight k, I mean one associated
to the representation of
rho_k: GL_n-1 x GL_1 --> GL_1
given by rho_k(A,r) = r^k. Shimura, in his annals paper "The arithmetic of
Automorphic forms with respect to a unitary group" studies Eisenstein series
E_j,k, which when specialized to j = 0 give holomorphic automorphic forms of
weight k.
Do these series interpolate to give a measure on Z_p^x with values in p-adic
automorphic forms, in the same way that Katz interpolated classical
Eisenstein series in the modular case?
I know that Harris-Skinner-Li have constructed an Eisenstein measure, but my
impression is that it is for forms of U(n,n). Is there a way to "pull back"
their measure to induce an Eisenstein measure for a form of U(n-1,1), as in
my case?
Thanks,
Mark Behrens
