Automorphic forms and representations of p-adic groups

p 进群的自同构形式和表示

• 批准号: 14340011
• 负责人: SAITO Hiroshi
• 金额: $ 5.63万
• 依托单位: Graduate School of Science, Kyoto University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2002
• 资助国家: 日本
• 起止时间: 2002 至 2005
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-14340011/
• 关键词: restriction of representation; Blasius conjecture; special linear group; inner form; L-packet; multiplicity formula; automorphic induction; transfer factor; アーサーパケット; ユニタリ群; 安定跡公式; 特殊値; 宮脇予想; 特殊ユニタリ群; 誘導表現; グロス-プラサド予想; テータ対応; L-packet(エルパ

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.

关于 p-adic 群的可接受表示的限制，我们澄清了 Gelbart-Knapp 和 Henniart 的结果。同样在自守表示的限制上，我们改进了Labesse-Langlands的结果。利用这些结果，我们证明了Blasius关于一般线性群自同构表示限制的猜想。根据这些结果，我们确定了特殊线性群内部形式的调节L-包。在 2 级的情况下，Labesse 和 Langlands 证明了基本结果。但他们的结果在非分裂内部形式的情况下似乎并不自然。在实数群的情况下，利用Vogan的思想，给出了分量群的新定义，该定义将描述L-包的结构，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 对一般线性群自守归纳结果的推广。这个结果中同时描述所有内部形式的 L 包的想法是非常自然的，并且将为 L 包的未来研究提供一个清晰的观点。利用这些局部结果，我们给出了特殊内部形式的自同构表示的重数公式线性群。在不可分割的情况下，该公式是弱形式。要完成这一点与传输因子的自然定义有关，并且将是一个有趣的问题。

项目成果

Theta lifting of lowest weight modules and their associated cycles

最轻模块的 Theta 提升及其相关循环

• 发表时间: 2004
• 期刊: Duke Math. J. 125-3
• 作者: 西山 享

加藤 信一: "Whittaker-Shintani functions for orthogonal groups"Tohoku J.Math.. 55・1. 1-64 (2003)

加藤新一：“正交群的 Whittaker-Shintani 函数”Tohoku J.Math.. 55・1 (2003)。

Formulas for tamely ramified super ucspidal character of GL131

GL131 驯服分枝超 ucspidal 特征的公式

• 发表时间: 2003
• 期刊: Trans. Amer. Math. Soc. 355-2
• 作者: F.Hiai (with D.Petz;Y.Ueda);Kaoru Hiraga;Kyo Nishiyama;N.Obata (with A.Hora);齋藤 裕;N.Obata (with U.C.Ji);高橋 哲也
• 通讯作者: 高橋 哲也

齋藤 裕: "Convergence of the zeta functions of prehomogeneous vector spaces"Nagoya Math.J.. 170. 1-30 (2003)

Yutaka Saito：“预齐次向量空间的 zeta 函数的收敛性”Nagoya Math.J. 170. 1-30 (2003)

T.Konno: "Twisted endoscopy and the generic packet conjecture"Israel J.Math.. 129巻. 253-289 (2002)

T.Konno：“扭曲内窥镜检查和通用数据包猜想”Israel J.Math.. vol. 129. 253-289 (2002)