The Langlands Parameters of Subquotients of Certain Derived Functor Modules

LetGbe a noncompact, simple Lie group with finite center, letKbe a maximal compact subgroup, and let g0=k0⊕p0be the corresponding decomposition of the Lie algebra. Suppose rank G=rank K, and let t0be a compact Cartan subalgebra and b be a Borel subalgebra. LetAb(λ) be a derived functor module with infinitesimal characterλ+δwhich is nondominant with respect to a noncompact simple root. Suppose thatΛ=λ+2δ(p) isKdominant so that theKtype,τΛ, with highest weightΛoccurs with multiplicity one inAb(λ). We develop conditions on the roots of g under which a functor of cohomological induction maps a certain module of parabolic induction to another module of parabolic induction, extending a result due to Vogan. This allows us, in many cases, to determine the Langlands parameters of the subquotient ofAb(λ) containingτΛ, via a conjectured method of Knapp.