In this paper, we recover certain known results about the ladder
representations of GL(n, Q_p) defined and studied by Lapid, Minguez, and Tadic.
We work in the equivalent setting of graded Hecke algebra modules. Using the
Arakawa-Suzuki functor from category O to graded Hecke algebra modules, we show
that the determinantal formula proved by Lapid-Minguez and Tadic is a direct
consequence of the BGG resolution of finite dimensional simple gl(n)-modules.
We make a connection between the semisimplicity of Hecke algebra modules,
unitarity with respect to a certain hermitian form, and ladder representations.Comment: 14 page
