论典型单李群的Aq(λ)的Langlands参数

设G为具有有限中心的非紧致典型单李群且K为G的最大紧致子群.假定rank G=rank K 且G/K为非Hermitian对称.当Aq(λ)在弱好区之外,给出了G的Aq(λ)的L anglands参数.

On the Langlands parameters for Aq(λ) for classical simple Lie groups

Let G be a noncompact classical simple Lie group with finite center and K be its maximal compact subgroup.Letg0 be the Lie algebra of G and g be its complexification.Suppose that rankG=rankK,and that G/K is n ot Hermitian symmetric.For the (g,K) module Aq(λ) defined by,Knapp, they proposed a Conjectural Method for finding the Langlands parameter s for the natural irreducible constituent of Aq(λ) when λ is outside the weakly good range and proved that this Conjectural Method is successful whe n g0≌so(2m,2n),m,n＞1.In this paper it is proved that this Conjectural Me thod is successful for every noncompact classical simple groups.