The Restriction of Whittaker Modules to Certain Parabolic Subalgebras

Nolan R. Wallach
1981 Proceedings of the American Mathematical Society  
Certain twisted cohomology spaces of modules for the standard maximal parabolic subalgebra of âl(n, Q are studied. These results are shown to imply new proofs of results of Kostant on Whittaker modules in the special case of real forms of products of 3l(n, C)'s. 2. The study of certain modules. Let g be a semisimple Lie algebra over C. Let i) C 0 be a Cartan subalgebra. Let A be the root system of (g, b). Fix A+ to be a system of positive roots for A. Let n = 2oeA+ g", ñ = 2"eA+ Q-a-Set b = fj
more » ... eA+ Q-a-Set b = fj © ñ. Let ip: n -* C be a Lie algebra homomorphism. We assume that \j/ is generic. That is if a e A+ is simple then i//|ga ¥= 0.
doi:10.2307/2044189 fatcat:ok6tsuul6nfdbpyxnk6x54d6o4