Ladder representations of GL(n,Q_p)

2014/09/04 by Dan Barbasch, Barbasch, Dan, Dan Ciubotaru +1
Mathematics · #FOS: Mathematics #Representation Theory (math.RT) #math.RT

paper · pdf · doi:10.48550/arxiv.1409.1367

14 pages

arxiv created 2014/09/04 · arxiv updated 2014/09/05

Abstract

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.

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