Automorphic forms and representations of p-adic groups

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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.