Automorphic forms and representations of p-adic groups

关于p-Add群的可容许表示的限制，我们澄清了Gelbart-Knapp和Henniart的结果。此外，在自同构表示的限制下，我们改进了Labesse-Langland的结果。利用这些结果，我们证明了Blasius关于一般线性群的自同构表示的限制的猜想，并在此基础上确定了特殊线性群的内型的调和L-包。在二阶情形下，Labesse和Langland证明了基本结果。但在没有分裂的内部形态的情况下，他们的结果似乎并不自然。利用Vogan在实群情况下的思想，给出了描述L包结构的分支群的新定义，并确定了特殊线性群的所有内部形式的L包的结构。从技术上讲，我们的证明是基于Herb-Henniart关于一般线性群上自同构归纳的结果的推广。这一结果中同时刻画所有内形式的L-包的思想是非常自然的，这将为今后对L-包的研究提供一个明确的观点.利用这些局部结果，我们给出了特殊线性群的内形式的自同构表示的重数公式.在非分裂情况下，该公式是弱形式。要做到这一点，涉及到转移因子的自然定义，这将是一个有趣的问题。

On restriction of admissible representations of p-adic groups, we clarified the results by Gelbart-Knapp and Henniart. Also on the restriction of automorphic representations, we improved the result by Labesse-Langlands. Using these results, we proved the conjecture by Blasius on the restriction of automorphic representations of general linear groups.Based on these results, we determined the tempered L-packets of inner forms of special linear groups. In the case of degree 2, Labesse and Langlands proved fundamental results. But their results in the case of non-split inner form does not seem natural. Using the idea of Vogan in the case of real groups, we gave a new definition of the component groups, which will describe the structure of L-packet, and determined the structure of L-packets of all inner forms of special linear groups. Technically, our proof is based on the generalization of the result by Herb-Henniart on automorphic induction on general linear groups. The idea in this result to describe L-packets simultaneously for all inner form is very natural and will give a clear viewpoint for future investigation of L-packets.Using these local results, we gave a multiplicity formula for automorphic representations for inner forms of special linear groups. In the non-split cases, the formula is a weak form. To complete this is related to a natural definition of transfer factor and will be an interesting problem.