Langlands parameters of derived functor modules and Vogan diagrams - Friedman, Paul D. (MATHEMATICA SCANDINAVICA, 2003)
Let G be a linear reductive Lie group with finite center, let K be a maximal compact subgroup, and assume that rank G = rank K. Let g= lu be a θ stable parabolic subalgebra obtained by building l from a subset of the compact simple roots and form A_g(λ). Suppose Λ=λ+2δ( up) is K-dominant and the infinitesimal character, λ+δ, of A_g(λ) is nondominant due to a noncompact simple root. By interpreting these conditions on the level of Vogan diagrams, a conjecture by Knapp is (essentially) settled for the groups G=SU(p,q), Sp(p,q), and SO^*(2n), thereby determining the Langlands parameters of natural irreducible subquotient of A_ g(λ). For the remaining classical groups, simple supplementary conditions are given under which the Langlands parameters may be determined.