论连通和单连通可裂G_2的A_q(λ)的酉性

ON THE UNITARIZABILITY FOR Aq(λ) for CONNECTED AND SIMPLY-CONNECTED SPLIT G2

设G为一连通,单连通的G2型可裂实李群,K为G的最大紧致子群,g为G的李代数的复化,Aq（λ）为 Knapp在[7]中的定义（g,K）-模.（MAN,σ,υ）表示由[7]中猜测方法确定的Aq（λ）的自然不可约分量的Langlands参数.本文确定了当λ位于弱好区域外时,哪些Langlands商J（MAN,σ,υ）为酉的.

Let G be a connected, simply-connected split real Lie group of type G2, and K a maximal compact subgroup of G. Let g be the complexification of the Lie algebra of G and Aq(λ) the (g, K)-module defined by Knapp[7]. Let (MAN, σ, v) be the Langlands parameters of the natural irreducible constituent of Aq(λ) determined by the Conjectural Method given by [7].The authors determine which Langlands quotients J(MAN,σ,v) are unitary when A is outside the weakly good range.