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In this paper, we recover certain known results about the ladderrepresentations 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 theArakawa-Suzuki functor from category O to graded Hecke algebra modules, we showthat the determinantal formula proved by Lapid-Minguez and Tadic is a directconsequence 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.

Ladder representations of GL(n,Q_p)