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Some remarks on the automorphic spectrum of the inner forms of SL(N) (保型表現とその周辺 : RIMS研究集会報告集)
| Content Provider | Semantic Scholar |
|---|---|
| Author | Li, Wen-Wei |
| Copyright Year | 2013 |
| Abstract | In this survey article, we start by reviewing Arthur’s conjectures for the multiplicities of -automorphic representations in the discrete spectrum. We also give a sketch of the main ideas thereof, as exemplified in Arthur’s endoscopic classification for classical groups, and then discuss its relation with the Hiraga-Saito theory for the group $SL(N)$ and its inner forms. This is based on a talk given in the RIMS workshop “Automorphic Representations and Related Topics”, Kyoto $2013$ . 1 Multiplicities in the discrete spectrum Let $F$ be a number field and $\mathbb{A}$ $:=\mathbb{A}_{F}$ its ring of ad\‘eles. Fix an algebraic closure $F$ of $F$ . We define $\Gamma_{F}$ $:=$ Gal $(\overline{F}/F)$ and denote its Weil group by $W_{F}$ . The Weil-Deligne group of $F$ is denoted by $W_{F}’.$ For a connected reductive $F$-group $G$ , one of the main concerns of the theory of -automorphic forms is to study the right regular representation of $G(\mathbb{A})$ on $L^{2}(G(F)\backslash G(\mathbb{A})^{1})=L_{disc}^{2}(G(F)\backslash G(\mathbb{A})^{1})\oplus$ (continuous spectrum) where $G(\mathbb{A})^{1}$ is the kernel of the Harish-Chandra homomorphism $H_{G}$ : $G(\mathbb{A})arrow$ |
| Starting Page | 65 |
| Ending Page | 74 |
| Page Count | 10 |
| File Format | PDF HTM / HTML |
| Volume Number | 1871 |
| Alternate Webpage(s) | http://www.kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/contents/pdf/1871-08.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
