2005 Fiscal Year Final Research Report Summary
Automorphic forms and representations of p-adic groups
| Project/Area Number |
14340011
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Graduate School of Science, Kyoto University |
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Principal Investigator |
SAITO Hiroshi Kyoto University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (20025464)
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| Co-Investigator(Kenkyū-buntansha) |
KATO Shin-ichi Kyoto University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (90114438)
MATSUKI Toshihiko Kyoto University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (20157283)
IKEDA Tamotsu Kyoto University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (20211716)
NISHIYAMA Kyo Kyoto University, Graduate School of Science, Associate Professor, 大学院・理学研究科, 助教授 (70183085)
HIRAGA Kaoru Kyoto University, Graduate School of Science, Lecturer, 大学院・理学研究科, 講師 (10260605)
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| Project Period (FY) |
2002 – 2005
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| Keywords | restriction of representation / Blasius conjecture / special linear group / inner form / L-packet / multiplicity formula / automorphic induction / transfer factor |
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| Research Abstract |
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.
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