论文标题
重新定性cuspidales de gl（r，d）区分par une contrieintérieure
Représentations cuspidales de GL(r,D) distinguées par une involution intérieure
论文作者
论文摘要
令n为正整数，f为奇数残基特征p和g的非架构局部紧凑场是GL（2n，f）的内部形式。这是一组形式的GL（R，d），用于降低D度的正整数R和disture F-Elgebra d，因此rd = 2n。令k为大小为r的代数中f的二次扩展，d中的系数为d，而h是G中的centralizer。我们从类型理论的角度研究了G的自我尖锐表示G及其对H的区分。鉴于G的这种表示PI，我们计算了langlands参数PHI pHi phi对k的Weil组限制的Epsilon因子的1/2的值，表示E（K，Phi）。 当f具有特征0时，我们推断出Pi在且仅当Phi是symbletic和e（k，phi）=（-1）^r时才会h-Disting。在这种情况下，这证明了Prasad和Takloo-Bighash的猜想。
Let n be a positive integer, F be a non-Archimedean locally compact field of odd residue characteristic p and G be an inner form of GL(2n,F). This is a group of the form GL(r,D) for a positive integer r and division F-algebra D of reduced degree d such that rd=2n. Let K be a quadratic extension of F in the algebra of matrices of size r with coefficients in D, and H be its centralizer in G. We study selfdual cuspidal representations of G and their distinction by H from the point of view of type theory. Given such a representation pi of G, we compute the value at 1/2 of the epsilon factor of the restriction of the Langlands parameter phi of pi to the Weil group of K, denoted e(K,phi). When F has characteristic 0, we deduce that pi is H-distinguished if and only if phi is symplectic and e(K,phi)=(-1)^r. This proves in this case a conjecture by Prasad and Takloo-Bighash.
